Spectral Properties Of Noncommuting Operators

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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 Properties Of Noncommuting Operators

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Author : Brian R. Jefferies
language : en
Publisher:
Release Date : 2014-01-15

Spectral Properties Of Noncommuting Operators written by Brian R. Jefferies and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

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 Theory Of Non Commutative Harmonic Oscillators An Introduction

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Author : Alberto Parmeggiani
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-22

Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction written by Alberto Parmeggiani 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 2010-04-22 with Mathematics categories.

This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.

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.

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.

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.

Phase In Optics

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Author : Myron W Evans
language : en
Publisher: World Scientific
Release Date : 1998-10-05

Phase In Optics written by Myron W Evans and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-05 with Science categories.

This book is devoted to the classical and quantum phases in wave and particle optics from the viewpoint of both theory and applications. Wave and beam light optics are reviewed in considerable detail, featuring optical imaging and holography in linear optics and phase conjugation methods in nonlinear optics. Photon optics is embodied here as quantum optics with the modes treated as quantum harmonic oscillators. The importance of the Wigner function for the phase space description in the context of canonical quantization is respected and the method of quasidistributions related to operator orderings in the second-quantized theory is exposed. The history of the quantum phase problem, characterized by renewed interest in the solution to the problem, is included and brought up to date. Approaches based on exponential phase operators, discrete phase states, the enlargement of the Hilbert space of the harmonic oscillator leading to the phase representations and distributions, together with solutions motivated by the quasidistributions, are introduced. The operational approach to the quantum phase is contrasted with the previous formalisms. The results of the study of the coherent states and the ordinary squeezed states from the viewpoint of the quantum phase and those of the analysis of the quantum statistics of phase-related special states of the light field are provided. The quantum phase is also treated with respect to quantum interferometry, particle interferometry, nonlinear optical processes, and quantum nondemolition measurements.The book will prove indispensable to research workers in general optics, quantum optics and electronics, optoelectronics, and nonlinear optics, as well as to students of physics, optics, optoelectronics, photonics, and optical engineering.

Operator Theory In Harmonic And Non Commutative Analysis

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Author : Joseph A. Ball
language : en
Publisher: Springer
Release Date : 2014-06-21

Operator Theory In Harmonic And Non Commutative Analysis written by Joseph A. Ball and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-21 with Mathematics categories.

This book contains the proceedings of the 23rd International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012. It includes twelve articles presenting both surveys of current research in operator theory and original results.

Noncommutative Geometry And The Standard Model Of Elementary Particle Physics

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Author : Florian Scheck
language : en
Publisher: Springer
Release Date : 2008-01-11

Noncommutative Geometry And The Standard Model Of Elementary Particle Physics written by Florian Scheck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.

The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.