Steffen Roch's Books

Limit Operators and Their Applications in Operator Theory

By: Vladimir Rabinovich,Steffen Roch,Bernd Silbermann

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Limit Operators and Their Applications in Operator Theory

By: Vladimir Rabinovich,Steffen Roch,Bernd Silbermann

This is the first monograph devoted to a fairly wide class of operators, namely band and band-dominated operators and their Fredholm theory. The main tool in studying this topic is limit operators. Applications are presented to several important classes of such operators: convolution type operators and pseudo-differential operators on bad domains and with bad coefficients.

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Page Count

404

Publisher

Birkhäuser

Published Date

ISBN 10

3034879113

ISBN 13

9783034879118

C* - Algebras and Numerical Analysis

By: Ronald Hagen,Steffen Roch,Bernd Silbermann

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C* - Algebras and Numerical Analysis

By: Ronald Hagen,Steffen Roch,Bernd Silbermann

Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more.

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Page Count

388

Publisher

CRC Press

Published Date

ISBN 10

0824704606

ISBN 13

9780824704605

Spectral Theory of Approximation Methods for Convolution Equations

By: Roland Hagen,Steffen Roch,Bernd Silbermann

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Spectral Theory of Approximation Methods for Convolution Equations

By: Roland Hagen,Steffen Roch,Bernd Silbermann

The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.

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Page Count

388

Publisher

Birkhäuser

Published Date

ISBN 10

3034890672

ISBN 13

9783034890670

Non-commutative Gelfand Theories

A Tool-kit for Operator Theorists and Numerical Analysts

By: Steffen Roch,Pedro A. Santos,Bernd Silbermann

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Non-commutative Gelfand Theories

A Tool-kit for Operator Theorists and Numerical Analysts

By: Steffen Roch,Pedro A. Santos,Bernd Silbermann

Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.

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Page Count

388

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0857291831

ISBN 13

9780857291837

Defining a British State

Treason and National Identity, 1608-1820

By: L. Steffen

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Defining a British State

Treason and National Identity, 1608-1820

By: L. Steffen

Explores the formation of the British state and national identity from 1603-1820 by examining the definitions of sovereignty and allegiance presented in treason trials. The king's person remained central to national identity and the state until republican challenges forced prosecutors in treason trials to innovate and redefine sovereign authority.

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Page Count

256

Publisher

Springer

Published Date

ISBN 10

0230513751

ISBN 13

9780230513754

Calculus of Variations and Geometric Evolution Problems

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetaro, Italy, June 15-22, 1996

By: F. Bethuel,G. Huisken,S. Mueller,K. Steffen

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Calculus of Variations and Geometric Evolution Problems

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetaro, Italy, June 15-22, 1996

By: F. Bethuel,G. Huisken,S. Mueller,K. Steffen

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

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Page Count

299

Publisher

Springer

Published Date

ISBN 10

3540488138

ISBN 13

9783540488132

Structure and Evolution of Invertebrate Nervous Systems

By: Andreas Schmidt-Rhaesa,Steffen Harzsch,Günter Purschke

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Structure and Evolution of Invertebrate Nervous Systems

By: Andreas Schmidt-Rhaesa,Steffen Harzsch,Günter Purschke

The nervous system is particularly fascinating for many biologists because it controls animal characteristics such as movement, behavior, and coordinated thinking. Invertebrate neurobiology has traditionally been studied in specific model organisms, whilst knowledge of the broad diversity of nervous system architecture and its evolution among metazoan animals has received less attention. This is the first major reference work in the field for 50 years, bringing together many leading evolutionary neurobiologists to review the most recent research on the structure of invertebrate nervous systems and provide a comprehensive and authoritative overview for a new generation of researchers. Presented in full colour throughout, Structure and Evolution of Invertebrate Nervous Systems synthesizes and illustrates the numerous new findings that have been made possible with light and electron microscopy. These include the recent introduction of new molecular and optical techniques such as immunohistochemical staining of neuron-specific antigens and fluorescence in-situ-hybridization, combined with visualization by confocal laser scanning microscopy. New approaches to analysing the structure of the nervous system are also included such as micro-computational tomography, cryo-soft X-ray tomography, and various 3-D visualization techniques. The book follows a systematic and phylogenetic structure, covering a broad range of taxa, interspersed with chapters focusing on selected topics in nervous system functioning which are presented as research highlights and perspectives. This comprehensive reference work will be an essential companion for graduate students and researchers alike in the fields of metazoan neurobiology, morphology, zoology, phylogeny and evolution.

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Page Count

761

Publisher

Oxford University Press

Published Date

ISBN 10

0191504742

ISBN 13

9780191504747

C* - Algebras and Numerical Analysis

By: Ronald Hagen,Steffen Roch,Bernd Silbermann

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C* - Algebras and Numerical Analysis

By: Ronald Hagen,Steffen Roch,Bernd Silbermann

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Page Count

388

Publisher

CRC Press

Published Date

ISBN 10

0824704606

ISBN 13

9780824704605

Finite Sections of Band-Dominated Operators

By: Steffen Roch

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Finite Sections of Band-Dominated Operators

By: Steffen Roch

Intends to review the advances and to present the results in the numerical analysis of the finite sections method for general band and band-dominated operators. This title addresses topics such as the stability of the finite sections method and the asymptotic behavior of singular values.

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