Palle Jorgensen's Books

Harmonic Analysis

By: Palle E.T. Jorgensen

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There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.

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281

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470448807

ISBN 13

9781470448806

Operators and Representation Theory

Canonical Models for Algebras of Operators Arising in Quantum Mechanics

By: Palle E.T. Jorgensen

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Operators and Representation Theory

Canonical Models for Algebras of Operators Arising in Quantum Mechanics

By: Palle E.T. Jorgensen

Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

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307

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Courier Dover Publications

Published Date

ISBN 10

0486822575

ISBN 13

9780486822570

Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator

Functions which are Harmonic with Respect to a Transfer Operator

By: Palle E. T. Jørgensen

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Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator

Functions which are Harmonic with Respect to a Transfer Operator

By: Palle E. T. Jørgensen

Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently

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American Mathematical Soc.

Published Date

ISBN 10

0821826883

ISBN 13

9780821826881

Representation Theory and Numerical AF-Invariants

The Representations and Centralizers of Certain States on Od

By: Ola Bratteli,Palle E. T. Jørgensen,Vasylʹ Ostrovsʹkyĭ

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Representation Theory and Numerical AF-Invariants

The Representations and Centralizers of Certain States on Od

By: Ola Bratteli,Palle E. T. Jørgensen,Vasylʹ Ostrovsʹkyĭ

Part A. Representation theory Part B. Numerical AF-invariants Bibliography List of figures List of tables List of terms and symbols.

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202

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American Mathematical Soc.

Published Date

ISBN 10

0821834916

ISBN 13

9780821834916

Iterated Function Systems, Moments, and Transformations of Infinite Matrices

By: Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman

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Iterated Function Systems, Moments, and Transformations of Infinite Matrices

By: Palle E. T. Jørgensen,Keri A. Kornelson,Karen L. Shuman

The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.

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122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852485

ISBN 13

9780821852484

Iterated Function Systems and Permutation Representations of the Cuntz Algebra

By: Ola Bratteli,Palle E. T. Jørgensen

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Iterated Function Systems and Permutation Representations of the Cuntz Algebra

By: Ola Bratteli,Palle E. T. Jørgensen

This book is intended for graduate students and research mathematicians working in functional analysis.

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106

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American Mathematical Soc.

Published Date

ISBN 10

0821809628

ISBN 13

9780821809624

Wavelets, Frames and Operator Theory

Focused Research Group Workshop on Wavelets, Frames, and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland

By: Palle E. T. Jørgensen,David R. Larson

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Wavelets, Frames and Operator Theory

Focused Research Group Workshop on Wavelets, Frames, and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland

By: Palle E. T. Jørgensen,David R. Larson

Nineteen papers are presented from a special joint session held in conjunction with the American Mathematical Society's 2003 annual meeting in Baltimore, and a National Science Foundation workshop at the University of Maryland. The papers distinguish themselves by often including applications as wel

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358

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American Mathematical Soc.

Published Date

ISBN 10

0821833804

ISBN 13

9780821833803

Wavelets Through a Looking Glass

The World of the Spectrum

By: Ola Bratteli,Palle E. T. Jørgensen

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Wavelets Through a Looking Glass

The World of the Spectrum

By: Ola Bratteli,Palle E. T. Jørgensen

This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.

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424

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Springer Science & Business Media

Published Date

ISBN 10

0817642803

ISBN 13

9780817642808

Analysis and Probability

Wavelets, Signals, Fractals

By: Palle E. T. Jorgensen

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Analysis and Probability

Wavelets, Signals, Fractals

By: Palle E. T. Jorgensen

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

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320

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Springer Science & Business Media

Published Date

ISBN 10

0387330828

ISBN 13

9780387330822

Gudme

Iron Age Settlement and Central Halls

By: Palle Østergaard Sørensen

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Gudme

Iron Age Settlement and Central Halls

By: Palle Østergaard Sørensen

Gudme: The Iron Age Settlement and Central Halls presents, describes and interprets the many finds and structures that have been comprised during the extended excavations at the central parts of the Gudme locality on southeast Funen, Denmark. Head of excavation Palle Østergaard Sørensen extracts, combines, classifies, dates and temporalizes the many finds and houses from the excavations Gudmehallerne, Gudme III, Gudme IV. Since the 19th century the Gudme area has been known as one of the richest prehistoric localities in Scandinavia, and more than 1,000 roman coins, close to 600 fibulas as well as several small mask and animal figurines form part of the Gudme find assemblage. From AD 200 to AD 600 the site expanded rapidly and covered as much as one square kilometer comprising up to 50 farmsteads. At the individual farms, specialized craftsmanship can be found and the debris and tools of gold- and silversmiths as well as bronze casting is abundant here, bronze fragments, often from statues, imported from the Roman Empire form a distinct category of finds bearing witness to a flourishing and innovative world of craftsmanship, as well as an extensive trade network. During this period the unique and monumental halls, with the largest being 47 m long and 10 m wide, dominated the hilltops east of Gudme lake. Just to the south a smaller building accompanied the large hall, and had been purposely demolished and rebuilt several times at the exact same spot. The unusually large entrances to the two adjoined buildings lead straight from one to the other, thus witnessing a duality of buildings that came to define the aristocratic localities throughout Scandinavia in the following 800 years. Hence, Gudme represents a starting point for a significant type of architectural ideal as well as a first generation of central places.

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399

Publisher

Oxbow Books

Published Date

ISBN 10

1789259096

ISBN 13

9781789259094

Megaliths and rituals at Tustrup, Denmark

By: Palle Eriksen,Anne Birgitte Gebauer,Torsten Madsen

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Megaliths and rituals at Tustrup, Denmark

By: Palle Eriksen,Anne Birgitte Gebauer,Torsten Madsen

The complex of megaliths near Tustrup is a prime example of the megalithic sites used by early farming communities in Stone Age Europe. Excavated in the 1950s by Moesgaard Museum, the site continues to hold great contemporary and scientific value. Its significance relates primarily to the unusual find of a ritual complex connected to two dolmens and passage grave. The question of why monumental sites played such an important role for early farming communities is currently the focus of several international studies. In Denmark, which boasts one of the world’s largest concentrations of megalithic monuments as well as a strong tradition for research in the area, archaeologists have had a longstanding wish to contribute to this discussion with a comprehensive publication about the unique complex of megaliths near Tustrup. Experts have researched the finds and meticulously analysed the site and its artefacts. These detailed studies have led to surprising and well-documented interpretations of the megalithic tombs, the construction history of the ritual site and their function, along with the inter-relationship between the monuments.

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487

Publisher

Aarhus Universitetsforlag

Published Date

ISBN 10

8793423918

ISBN 13

9788793423916

Extensions of Positive Definite Functions

Applications and Their Harmonic Analysis

By: Palle Jorgensen,Steen Pedersen,Feng Tian

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Extensions of Positive Definite Functions

Applications and Their Harmonic Analysis

By: Palle Jorgensen,Steen Pedersen,Feng Tian

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

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255

Publisher

Springer

Published Date

ISBN 10

331939780X

ISBN 13

9783319397801

Recent Advances in Computational Sciences

Selected Papers from the International Workshop on Computational Sciences and Its Education, Beijing, China, 29-31 August 2005

By: Palle E. T. J?rgensen,Xiaoping Shen,Chiwang Shu

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Recent Advances in Computational Sciences

Selected Papers from the International Workshop on Computational Sciences and Its Education, Beijing, China, 29-31 August 2005

By: Palle E. T. J?rgensen,Xiaoping Shen,Chiwang Shu

This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrdinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book.This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.

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Page Count

395

Publisher

World Scientific

Published Date

ISBN 10

981270700X

ISBN 13

9789812707000

Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.

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449

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World Scientific

Published Date

ISBN 10

9811265534

ISBN 13

9789811265532

Non-commutative Analysis

By: Palle Jorgensen,Feng Tian

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Non-commutative Analysis

By: Palle Jorgensen,Feng Tian

This is a book to be read and worked with. For a beginning graduate student, this can be a valuable experience which at some points in fact leads up to recent research. For such a reader there is also historical information included and many comments aiming at an overview. It is inspiring and original how old material is combined and mixed with new material. There is always something unexpected included in each chapter, which one is thankful to see explained in this context and not only in research papers which are more difficult to access.'Mathematical Reviews ClippingsThe book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

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562

Publisher

World Scientific

Published Date

ISBN 10

9813202149

ISBN 13

9789813202146

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

By: Palle Jorgensen,James Tian

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

By: Palle Jorgensen,James Tian

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

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253

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World Scientific

Published Date

ISBN 10

9811225796

ISBN 13

9789811225796

Mathematics Of Multilevel Systems: Data, Scaling, Images, Signals, And Fractals

By: Palle Jorgensen,Myung-sin Song

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Mathematics Of Multilevel Systems: Data, Scaling, Images, Signals, And Fractals

By: Palle Jorgensen,Myung-sin Song

This book presents the mathematics of wavelet theory and its applications in a broader sense, comprising entropy encoding, lifting scheme, matrix factorization, and fractals. It also encompasses image compression examples using wavelet transform and includes the principal component analysis which is a hot topic on data dimension reduction in machine learning.Readers will find equal coverage on the following three themes:The book entails a varied choice of diverse interdisciplinary themes. While the topics can be found in various parts of the pure and applied literature, this book fulfills the need for an accessible presentation which cuts across the fields.As the target audience is wide-ranging, a detailed and systematic discussion of issues involving infinite dimensions and Hilbert space is presented in later chapters on wavelets, transform theory and, entropy encoding and probability. For the problems addressed there, the case of infinite dimension will be more natural, and well-motivated.

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Page Count

270

Publisher

World Scientific

Published Date

ISBN 10

9811269017

ISBN 13

9789811269011

Operators and Representation Theory

Canonical Models for Algebras of Operators Arising in Quantum Mechanics

By: Palle E.T. Jorgensen

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Operators and Representation Theory

Canonical Models for Algebras of Operators Arising in Quantum Mechanics

By: Palle E.T. Jorgensen

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Page Count

307

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486822575

ISBN 13

9780486822570

Mathematics Of Multilevel Systems: Data, Scaling, Images, Signals, And Fractals

By: Palle Jorgensen,Myung-sin Song

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Mathematics Of Multilevel Systems: Data, Scaling, Images, Signals, And Fractals

By: Palle Jorgensen,Myung-sin Song

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270

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World Scientific

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ISBN 10

9811269017

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9789811269011

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

By: Palle Jorgensen,James Tian

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

By: Palle Jorgensen,James Tian

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253

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World Scientific

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ISBN 10

9811225796

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9789811225796

Analysis and Probability

Wavelets, Signals, Fractals

By: Palle E. T. Jorgensen

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Analysis and Probability

Wavelets, Signals, Fractals

By: Palle E. T. Jorgensen

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320

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Springer Science & Business Media

Published Date

ISBN 10

0387330828

ISBN 13

9780387330822

Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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Operator Theory And Analysis Of Infinite Networks

By: Palle Jorgensen,Erin P J Pearse

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449

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World Scientific

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ISBN 10

9811265534

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9789811265532

Extensions of Positive Definite Functions

Applications and Their Harmonic Analysis

By: Palle Jorgensen,Steen Pedersen,Feng Tian

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Extensions of Positive Definite Functions

Applications and Their Harmonic Analysis

By: Palle Jorgensen,Steen Pedersen,Feng Tian

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255

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Springer

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ISBN 10

331939780X

ISBN 13

9783319397801

Non-commutative Analysis

By: Palle Jorgensen,Feng Tian

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Non-commutative Analysis

By: Palle Jorgensen,Feng Tian

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562

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World Scientific

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ISBN 10

9813202149

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9789813202146

Harmonic Analysis

By: Palle E.T. Jorgensen

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Harmonic Analysis

By: Palle E.T. Jorgensen

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281

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American Mathematical Soc.

Published Date

ISBN 10

1470448807

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9781470448806

Algebraic Methods in Operator Theory

By: Raul E. Curto,Palle Jorgensen

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Algebraic Methods in Operator Theory

By: Raul E. Curto,Palle Jorgensen

The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify ing theme is the algebraic view and approach to the study of operators and their applications. The complementarity between the diversity of topics on the one hand and the unity of ideas on the other has been stressed. Some of the longer contributions represent material from lectures (in expanded form and with proofs for the most part). However, the shorter papers, as well as the longer ones, are an integral part of the picture; they have all been carefully refereed and revised with a view to a unity of purpose, timeliness, readability, and broad appeal. Raul Curto and Paile E. T.

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376

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Springer Science & Business Media

Published Date

ISBN 10

0817637451

ISBN 13

9780817637453

Wavelets Through a Looking Glass

The World of the Spectrum

By: Ola Bratteli,Palle E. T. Jørgensen

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Wavelets Through a Looking Glass

The World of the Spectrum

By: Ola Bratteli,Palle E. T. Jørgensen

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424

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Springer Science & Business Media

Published Date

ISBN 10

0817642803

ISBN 13

9780817642808

Operator Theory, Operator Algebras, and Applications

The 25th Great Plains Operator Theory Symposium, June 7-12, 2005, University of Central Florida, Florida

By: Deguang Han,Palle E. T. Jørgensen,David R. Larson

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Operator Theory, Operator Algebras, and Applications

The 25th Great Plains Operator Theory Symposium, June 7-12, 2005, University of Central Florida, Florida

By: Deguang Han,Palle E. T. Jørgensen,David R. Larson

This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.

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Page Count

440

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839233

ISBN 13

9780821839232

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