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Banach Algebra Techniques in Operator Theory
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Ronald G Douglas
Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in ...
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Elements of Operator Theory
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Carlos S Kubrusly
This book is aimed at a new generation of researchers and graduate students in the field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert Spaces, culminating with the Spectral Theorem, one of the landmarks ...
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Spectral Theory of Operators in Hilbert Space
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K. O. Friedrichs
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Holomorphic Spaces
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Sheldon Axler (Editor), John E McCarthy (Editor), Donald Sarason (Editor)
Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains ...
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Pseudodifferential analysis on symmetric cones
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Unterberger, Upmeier 1950-
Symmetric cones, possibly disguised under non-linear changes of coordinates, are the building blocks of manifolds with edges, corners, or conical points of a very general nature. Besides being a canonical open set of some Euclidean space, a symmetric cone L has an intrinsic Riemannian structure of its own, turning it into a symmetric space. These ...
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Wavelets and Operators: Volume 1
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by
Yves Meyer
The strength of wavelets lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in any fields where an approach to transient behavior is needed. The aim of this book is to describe the foundations of the so-called wavelet analysis, emphasizing its roots in ...
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Basic Operator Theory
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Israel Gohberg, Seymour Goldberg
"Basic Operator Theory" provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, "Basic Operator Theory" begins with the geometry of ...
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Realizability Theory for Continuous Linear Systems
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A. H. Zemanian
Concise exposition of realizability theory as applied to continous linear systems, specifically to the operators generated by physical systems as mappings of stimuli into responses. Many problems included.
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Operators, Functions, and Systems: An Easy Reading
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N K Nikol'skii
This unique work combines together in two volumes four formally distinct topics of modern analysis and its applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators; function models for linear operators and free interpolations; and, infinite-dimensional system theory and signal processing. "Volume 1, ...
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Operator Theory for Electromagnetics: An Introduction
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George W Hanson, Alexander B Yakovlev
While there are many excellent books available on fundamental and applied electromagnetics, few discuss the subject from the view of operator theory, introducing operator theory only when needed. Perhaps this is because the operators associated with dynamic problems are commonly thought to be not well behaved. This is, however, not the case, and ...
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Introduction to Banach Algebras, Operators, and Harmonic Analysis
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by
Garth Dales, Pietro Aiena, Jorg Eschmeier
This work has arisen from lecture courses given by the authors on important topics within functional analysis. The authors, who are all leading researchers, give introductions to their subjects at a level ideal for beginning graduate students, and others interested in the subject. The collection has been carefully edited so as to form a coherent ...
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An Introduction to Operators on the Hardy-Hilbert Space
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by
Peter Rosenthal, Ruben A Martinez-Avendano, Rubn A Martinez-Avendano
The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of ...
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Operator Algebras in Dynamical Systems
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Shoichiro Sakai, Shtichirt Sakai
This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum ...
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Applications of Functional Analysis and Operator Theory
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by
V Hutson
Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential ...
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Spectral Theory of Linear Operators: And Spectral Systems in Banach Algebras
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by
Vladimir Muller
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their ...
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Determining Spectra in Quantum Theory
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Maddaly Krishna, Michael Demuth
The spectral theory of Schrodinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components a la Lebesgue decomposition. It contains a well-developed ...
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Eigenfunction expansions, operator algebras and Riemannian symmetric spaces
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by
Kauffman
This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized ...
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Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems
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Forester, Karl-Heinz Fvrster (Editor), Peter Jonas (Editor)
This volume contains a collection of recent original research papers in operator theory in Krein spaces, on generalized Nevanlinna functions, which are closely connected with this theory, and on nonlinear eigenvalue problems. Key topics: - spectral theory for normal operators in Krein spaces - perturbation theory for selfadjoint operators in Krein ...
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Operator Theory in Inner Product Spaces
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Karl-Heinz Frster (Editor), Peter Jonas (Editor), Heinz Langer (Editor)
This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including ...
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Operator Methods in Quantum Mechanics
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Martin Schechter
This text introduces techniques related to physical theory. Entire book is devoted to a particle moving in a straight line; students develop techniques by answering questions about the particle. 1981 edition.
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Hilbert Space Operators: A Problem Solving Approach
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Carlos S Kubrusly
This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state of the art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space ...
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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator
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by
J J Duistermaat
This work uses the heat kernal theory of Berline-Getzler-Vergne to focus on the special case of the spin-c Dirac operators on almost complex manifolds. A large part of the text has a wider scope than spin-c Dirac, such as the asymptotic expansion of heat kernels for generalized Laplace operators.
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Spectral decompositions and analytic sheaves
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Eschmeier, Putinar
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, classical results from the cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the ...
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Non-relativistic quantum dynamics
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by
Werner O Amrein
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Entropy, Compactness and the Approximation of Operators
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by
Bernd Carl, Irmtraud Stephani
Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the relations between compactness and other analytical properties, e.g. approximability and eigenvalue ...
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