A Spectral Theory Of Noncommuting Operators

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A Spectral Theory Of Noncommuting Operators

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Author : Rongwei Yang
language : en
Publisher: Springer Nature
Release Date : 2024-03-25

A Spectral Theory Of Noncommuting Operators written by Rongwei Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-25 with Mathematics categories.

The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.

Spectral Properties Of Noncommuting Operators

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Author : Brian Jefferies
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-13

Spectral Properties Of Noncommuting Operators written by Brian Jefferies and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-13 with Computers categories.

Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.

Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras

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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.

Spectral Theory And Quantum Mechanics

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Author : Valter Moretti
language : en
Publisher: Springer
Release Date : 2018-01-30

Spectral Theory And Quantum Mechanics written by Valter Moretti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.

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."

Spectral Theory Mathematical System Theory Evolution Equations Differential And Difference Equations

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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-15

Spectral Theory Mathematical System Theory Evolution Equations Differential And Difference Equations written by Wolfgang Arendt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-15 with Mathematics categories.

The present volume contains a collection of original research articles and expository contributions on recent developments in operator theory and its multifaceted applications. They cover a wide range of themes from the IWOTA 2010 conference held at the TU Berlin, Germany, including spectral theory, function spaces, mathematical system theory, evolution equations and semigroups, and differential and difference operators. The book encompasses new trends and various modern topics in operator theory, and serves as a useful source of information to mathematicians, scientists and engineers.

Operator Calculus And Spectral Theory

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Author : M. Demuth
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Operator Calculus And Spectral Theory written by M. Demuth and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.

Spectral Theory On The S Spectrum For Quaternionic Operators

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Author : Fabrizio Colombo
language : en
Publisher: Springer
Release Date : 2019-01-04

Spectral Theory On The S Spectrum For Quaternionic Operators written by Fabrizio Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-04 with Mathematics categories.

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

Hypercomplex Analysis And Its Applications

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Author : Nelson Faustino
language : en
Publisher: Springer Nature
Release Date : 2025-07-02

Hypercomplex Analysis And Its Applications written by Nelson Faustino and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-02 with Mathematics categories.

This book contains a collection of short papers based on the presentations given at the international conference on Hypercomplex Analysis and its Applications celebrating Paula Cerejeiras’ 60th birthday. These papers present the latest results as well as overviews on specific topics in the areas of hypercomplex and harmonic analysis as well as their connections with partial differential equations and spectral theory.

Operator Theory Operator Algebras And Matrix Theory

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Author : Carlos André
language : en
Publisher: Birkhäuser
Release Date : 2018-08-22

Operator Theory Operator Algebras And Matrix Theory written by Carlos André and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-22 with Mathematics categories.

This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.

Feynman S Operational Calculus And Beyond

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Author : Gerald W Johnson
language : en
Publisher: OUP Oxford
Release Date : 2015-08-06

Feynman S Operational Calculus And Beyond written by Gerald W Johnson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with Science categories.

This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.