William Arveson's Books

Ten Lectures on Operator Algebras

By: William Arveson

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Ten Lectures on Operator Algebras

By: William Arveson

This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.

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108

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821889001

ISBN 13

9780821889008

Noncommutative Dynamics and E-Semigroups

By: William Arveson

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Noncommutative Dynamics and E-Semigroups

By: William Arveson

This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

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442

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Springer Science & Business Media

Published Date

ISBN 10

0387215247

ISBN 13

9780387215242

A Short Course on Spectral Theory

By: William Arveson

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A Short Course on Spectral Theory

By: William Arveson

This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

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143

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Springer Science & Business Media

Published Date

ISBN 10

0387215182

ISBN 13

9780387215181

Quantization, Nonlinear Partial Differential Equations, and Operator Algebra

1994 John Von Neumann Symposium on Quantization and Nonlinear Wave Equations June 7-11 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts

By: William Arveson,Thomas Branson,Irving Ezra Segal

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Quantization, Nonlinear Partial Differential Equations, and Operator Algebra

1994 John Von Neumann Symposium on Quantization and Nonlinear Wave Equations June 7-11 1994, Massachusetts Institute of Technology, Cambridge, Massachusetts

By: William Arveson,Thomas Branson,Irving Ezra Segal

This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties. Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrödinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.

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Page Count

239

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803816

ISBN 13

9780821803813

Operator Algebras and Quantum Statistical Mechanics

Volume 1: C*- and W*- Algebras. Symmetry Groups. Decomposition of States

By: Ola Bratteli,Derek William Robinson

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Operator Algebras and Quantum Statistical Mechanics

Volume 1: C*- and W*- Algebras. Symmetry Groups. Decomposition of States

By: Ola Bratteli,Derek William Robinson

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

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503

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Springer Science & Business Media

Published Date

ISBN 10

366202313X

ISBN 13

9783662023136

Operator Algebras and Quantum Statistical Mechanics 1

C*- and W*-Algebras. Symmetry Groups. Decomposition of States

By: Ola Bratteli,Derek William Robinson

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Operator Algebras and Quantum Statistical Mechanics 1

C*- and W*-Algebras. Symmetry Groups. Decomposition of States

By: Ola Bratteli,Derek William Robinson

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

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510

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Springer Science & Business Media

Published Date

ISBN 10

3662025205

ISBN 13

9783662025208

Ocean Ambient Noise

Measurement and Theory

By: William M. Carey,Richard B. Evans

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Ocean Ambient Noise

Measurement and Theory

By: William M. Carey,Richard B. Evans

This monograph develops the theory of noise mechanisms and measurements, and describes general noise characteristics and computational methods. The vast ambient noise literature is concisely summarized using theory combined with key representative results. The air sea boundary interaction zone is described in terms of nondimensional variables requisite for future experiments. Noise field coherency, rare directional measurements, and unique basin scale computations and methods are presented. The use of satellite measurements in these basin scale models is demonstrated. A series of appendices provides in-depth mathematical treatments which will be of interest to graduate students and active researchers.

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266

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Springer Science & Business Media

Published Date

ISBN 10

1441978321

ISBN 13

9781441978325

More Than Curious

A Science Memoir

By: William H. Press

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More Than Curious

A Science Memoir

By: William H. Press

The author found himself in places and times to closely observe significant events and noteworthy personalities in 20th century science. Variously, he interacted with such notables as Richard Feynman, S. Chandrasekhar, Edward Teller, Ya. B. Zel'dovich, John Wheeler, James Watson, Julian Schwinger, Fred Hoyle, Martin Rees, Stephen Hawking, Freeman Dyson, Ed Witten, and many others. His Ph.D. advisor, Kip Thorne, and his Ph.D. student, Adam Riess, each won Nobel Prizes-for discoveries that he helped them start. Later, he worked with (or for) not just scientists, but also technology capitalists and billionaires, admirals and generals, and political leaders including two U.S. presidents. His memoir is rich in stories about these people and events.

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695

Publisher

Darwin-Finch Publishing Company

Published Date

ISBN 13

9798989549719

Operator Theory, Analytic Functions, Matrices, and Electrical Engineering

By: J. William Helton

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Operator Theory, Analytic Functions, Matrices, and Electrical Engineering

By: J. William Helton

Expands the lectures given at a regional conference in Lincoln, Nebraska which brought together a wide variety of scientists, pure mathematicians and engineers.

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152

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821807188

ISBN 13

9780821807187

Mechanics of Flow-Induced Sound and Vibration, Volume 2

Complex Flow-Structure Interactions

By: William K. Blake

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Mechanics of Flow-Induced Sound and Vibration, Volume 2

Complex Flow-Structure Interactions

By: William K. Blake

Mechanics of Flow-Induced Sound and Vibration, Volume 2: Complex Flow-Structure Interactions, Second Edition, enables readers to fully understand flow-induced vibration and sound, unifying the disciplines of fluid dynamics, structural dynamics, vibration, acoustics, and statistics in order to classify and examine each of the leading sources of vibration and sound induced by various types of fluid motion. Starting from classical theories of aeroacoustics and hydroacoustics, a formalism of integral solutions valid for sources near boundaries is developed and then broadened to address different source types, including hydrodynamically induced cavitation and bubble noise, turbulent wall-pressure fluctuations, pipe and duct systems, lifting surface flow noise and vibration, and noise from rotating machinery. Each chapter is illustrated with comparisons of leading formulas and measured data. Combined with its companion book, Mechanics of Flow-Induced Sound and Vibration, Volume 1: General Concepts and Elementary Sources, the book covers everything an engineer needs to understand flow-induced sound and vibration. This book will be a vital source of information for postgraduate students, engineers and researchers with an interest in aerospace, ships and submarines, offshore structures, construction, and ventilation. - Presents every important topic in flow-induced sound and vibration - Covers all aspects of the topics addressed, from fundamental theory, to the analytical formulas used in practice - Provides the building blocks of computer modeling for flow-induced sound and vibration

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696

Publisher

Academic Press

Published Date

ISBN 10

0128122900

ISBN 13

9780128122907

Medical Malpractice

A Preventive Approach

By: William O. Robertson

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Medical Malpractice

A Preventive Approach

By: William O. Robertson

More than 90 percent of all the malpractice suits ever filed in the United States have been filed in the last two decades, a mere 3 percent of the nations history. And, currently, one out of every ten physicians in America is involved in an alleged incident of malpractice.This book addresses the distressing predicament facing both the doctor and the patient. Using a collection of case histories to explore the causes of malpractice, he offers sensible suggestions and guidelines for reducing both actual and perceived malpractice.

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236

Publisher

University of Washington Press

Published Date

ISBN 10

0295961627

ISBN 13

9780295961620

Introduction to Model Spaces and their Operators

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

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Introduction to Model Spaces and their Operators

By: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.

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339

Publisher

Cambridge University Press

Published Date

ISBN 10

1316390438

ISBN 13

9781316390436

Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra

By: William Norrie Everitt,Lawrence Markus

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Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra

By: William Norrie Everitt,Lawrence Markus

A multi-interval quasi-differential system $\{I_{r},M_{r},w_{r}:r\in\Omega\}$ consists of a collection of real intervals, $\{I_{r}\}$, as indexed by a finite, or possibly infinite index set $\Omega$ (where $\mathrm{card} (\Omega)\geq\aleph_{0}$ is permissible), on which are assigned ordinary or quasi-differential expressions $M_{r}$ generating unbounded operators in the Hilbert function spaces $L_{r}^{2}\equiv L^{2}(I_{r};w_{r})$, where $w_{r}$ are given, non-negative weight functions. For each fixed $r\in\Omega$ assume that $M_{r}$ is Lagrange symmetric (formally self-adjoint) on $I_{r}$ and hence specifies minimal and maximal closed operators $T_{0,r}$ and $T_{1,r}$, respectively, in $L_{r}^{2}$. However the theory does not require that the corresponding deficiency indices $d_{r}^{-}$ and $d_{r}^{+}$ of $T_{0,r}$ are equal (e. g. the symplectic excess $Ex_{r}=d_{r}^{+}-d_{r}^{-}\neq 0$), in which case there will not exist any self-adjoint extensions of $T_{0,r}$ in $L_{r}^{2}$. In this paper a system Hilbert space $\mathbf{H}:=\sum_{r\,\in\,\Omega}\oplus L_{r}^{2}$ is defined (even for non-countable $\Omega$) with corresponding minimal and maximal system operators $\mathbf{T}_{0}$ and $\mathbf{T}_{1}$ in $\mathbf{H}$. Then the system deficiency indices $\mathbf{d}^{\pm} =\sum_{r\,\in\,\Omega}d_{r}^{\pm}$ are equal (system symplectic excess $Ex=0$), if and only if there exist self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$ in $\mathbf{H}$. The existence is shown of a natural bijective correspondence between the set of all such self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$, and the set of all complete Lagrangian subspaces $\mathsf{L}$ of the system boundary complex symplectic space $\mathsf{S}=\mathbf{D(T}_{1})/\mathbf{D(T}_{0})$. This result generalizes the earlier symplectic version of the celebrated GKN-Theorem for single interval systems to multi-interval systems. Examples of such complete Lagrangians, for both finite and infinite dimensional complex symplectic $\mathsf{S}$, illuminate new phenoma for the boundary value problems of multi-interval systems. These concepts have applications to many-particle systems of quantum mechanics, and to other physical problems.

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American Mathematical Soc.

Published Date

ISBN 10

0821826697

ISBN 13

9780821826690

Operator Algebras and Quantum Statistical Mechanics II

Equilibrium States Models in Quantum Statistical Mechanics

By: Ola Bratteli,Derek William Robinson

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Operator Algebras and Quantum Statistical Mechanics II

Equilibrium States Models in Quantum Statistical Mechanics

By: Ola Bratteli,Derek William Robinson

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

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508

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662090899

ISBN 13

9783662090893

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

By: J. William Helton,Igor Klep,Scott McCullough,Markus Schweighofer

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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

By: J. William Helton,Igor Klep,Scott McCullough,Markus Schweighofer

An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→K such that C=V∗TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor ϑ(d), expressed as a ratio of Γ functions for d even, of all d×d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.

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118

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470434555

ISBN 13

9781470434557

Algebraic Topology

A First Course

By: William Fulton

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Algebraic Topology

A First Course

By: William Fulton

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

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435

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Springer Science & Business Media

Published Date

ISBN 10

1461241804

ISBN 13

9781461241805

Algebra

An Approach via Module Theory

By: William A. Adkins,Steven H. Weintraub

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Algebra

An Approach via Module Theory

By: William A. Adkins,Steven H. Weintraub

This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book). Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations. Why modules? The answer is that they are a basic unifying concept in mathematics. The reader is probably already familiar with the basic role that vector spaces play in mathematics, and modules are a generaliza tion of vector spaces. (To be precise, modules are to rings as vector spaces are to fields.

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540

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Springer Science & Business Media

Published Date

ISBN 10

1461209234

ISBN 13

9781461209232

Black Box Classical Groups

By: William M. Kantor,Ákos Seress

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Black Box Classical Groups

By: William M. Kantor,Ákos Seress

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.

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183

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821826190

ISBN 13

9780821826195

Introduction to Intersection Theory in Algebraic Geometry

By: William Fulton

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Introduction to Intersection Theory in Algebraic Geometry

By: William Fulton

Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. Suitable for graduate students in mathematics, this book describes the construction and computation of intersection products by means of the geometry of normal cones.

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American Mathematical Soc.

Published Date

ISBN 10

0821807048

ISBN 13

9780821807040

A Basic Course in Algebraic Topology

By: William S. Massey

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A Basic Course in Algebraic Topology

By: William S. Massey

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

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448

Publisher

Springer

Published Date

ISBN 10

1493990632

ISBN 13

9781493990634

Weakly Differentiable Functions

Sobolev Spaces and Functions of Bounded Variation

By: William P. Ziemer

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Weakly Differentiable Functions

Sobolev Spaces and Functions of Bounded Variation

By: William P. Ziemer

The term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func tions), have undergone considerable development during the past 20 years. From this development a rather complete theory has emerged and thus has provided the main impetus for the writing of this book. Since these classes of functions play a significant role in many fields, such as approximation theory, calculus of variations, partial differential equations, and non-linear potential theory, it is hoped that this monograph will be of assistance to a wide range of graduate students and researchers in these and perhaps other related areas. Some of the material in Chapters 1-4 has been presented in a graduate course at Indiana University during the 1987-88 academic year, and I am indebted to the students and colleagues in attendance for their helpful comments and suggestions.

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323

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461210151

ISBN 13

9781461210153

Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods

By: William Joseph Haboush

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Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods

By: William Joseph Haboush

Proceedings of a research institute held at Pennsylvania State University, July 1991, focusing on quantum and infinite-dimensional methods of algebraic groups. Topics include perverse sheaves, finite Chevalley groups, the general theory of algebraic groups, representations, invariant theory, general

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Page Count

429

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821815415

ISBN 13

9780821815410

Continuous Analogues of Fock Space

By: William Arveson

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Continuous Analogues of Fock Space

By: William Arveson

The problem of classifying semigroups of endomorphisms of type [italic]I[subscript]infinity symbol factors to outer conjugacy is reduced to the problem of classifying certain simpler structures associated to them, called product systems. Product systems are intimately connected with continuous tensor products of Hilbert spaces. We develop the general theory of product systems and give a number of applications to semigroups of endomorphisms of von Neumann algebras; in particular, we introduce a numerical invariant for such semigroups which is analogous to the Fredholm index.

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American Mathematical Soc.

Published Date

ISBN 10

0821824724

ISBN 13

9780821824726

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