Functional Analysis Spectral Theory

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer
Page : 614 pages
File Size : 40,7 Mb
Release : 2017-11-21
Category : Mathematics
ISBN : 9783319585406

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Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler,Thomas Ward Pdf

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

Author : V.S. Sunder
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,6 Mb
Release : 1997
Category : Mathematics
ISBN : 3764358920

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Functional Analysis by V.S. Sunder Pdf

In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter. There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these.

Author : Christophe Cheverry,Nicolas Raymond
Publisher : Springer Nature
Page : 258 pages
File Size : 45,7 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9783030674625

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A Guide to Spectral Theory by Christophe Cheverry,Nicolas Raymond Pdf

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Author : V. S. Sunder
Publisher : Unknown
Page : 306 pages
File Size : 47,6 Mb
Release : 1997
Category : Functional analysis
ISBN : 8185931143

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Functional Analysis - Spectral Theory by V. S. Sunder Pdf

Lectures given by the author at the Institute of Mathematical Sciences, Madras, in 1996.

Author : Julian Lopez-Gomez
Publisher : CRC Press
Page : 281 pages
File Size : 41,7 Mb
Release : 2001-03-28
Category : Mathematics
ISBN : 9781420035506

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Spectral Theory and Nonlinear Functional Analysis by Julian Lopez-Gomez Pdf

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators. Appealing to a broad audience, it contains many important contributions to linear algebra, linear functional analysis, nonlinear functional analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and systems. The results presented cover a thirty-year period and cut across a variety of mathematical fields.

Author : Vladimir Müller
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 52,5 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783764382650

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Spectral Theory of Linear Operators by Vladimir Müller Pdf

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 variants. Many results appear here for the first time in a monograph.

Author : David Borthwick
Publisher : Springer Nature
Page : 339 pages
File Size : 42,6 Mb
Release : 2020-03-12
Category : Mathematics
ISBN : 9783030380021

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Spectral Theory by David Borthwick Pdf

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.

Author : William Arveson
Publisher : Springer Science & Business Media
Page : 140 pages
File Size : 45,9 Mb
Release : 2001-11-09
Category : Mathematics
ISBN : 9780387953007

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A Short Course on Spectral Theory by William Arveson Pdf

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.

Author : Valter Moretti
Publisher : Springer
Page : 950 pages
File Size : 54,9 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319707068

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Spectral Theory and Quantum Mechanics by Valter Moretti Pdf

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Author : William Arveson
Publisher : Springer Science & Business Media
Page : 143 pages
File Size : 51,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215181

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A Short Course on Spectral Theory by William Arveson Pdf

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.

Author : Vladimir I. Bogachev,Oleg G. Smolyanov
Publisher : Springer Nature
Page : 586 pages
File Size : 54,7 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030382193

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Real and Functional Analysis by Vladimir I. Bogachev,Oleg G. Smolyanov Pdf

This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

Author : Sterling K. Berberian
Publisher : Unknown
Page : 138 pages
File Size : 44,7 Mb
Release : 1966
Category : Spectral theory (Mathematics)
ISBN : UCAL:B4405352

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Notes on Spectral Theory by Sterling K. Berberian Pdf

Author : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 50,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034877886

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Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras by Vladimir Müller Pdf

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 variants. Many results appear here for the first time in a monograph.

Author : Andrei Giniatoulline
Publisher : R.T. Edwards, Inc.
Page : 212 pages
File Size : 46,9 Mb
Release : 2005
Category : Mathematics
ISBN : 1930217099

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An Introduction to Spectral Theory by Andrei Giniatoulline Pdf

A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.

Author : Gilbert Helmberg
Publisher : Elsevier
Page : 362 pages
File Size : 48,6 Mb
Release : 2014-11-28
Category : Science
ISBN : 9781483164175

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Introduction to Spectral Theory in Hilbert Space by Gilbert Helmberg Pdf

North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.