II: Fourier Analysis, Self-Adjointness
Author: Michael Reed
Publisher: Elsevier
Published: 1975
Total Pages: 388
ISBN-13: 9780125850025
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Author: Michael Reed
Publisher: Elsevier
Published: 1975
Total Pages: 388
ISBN-13: 9780125850025
DOWNLOAD EBOOKBand 2.
Author: Michael Reed
Publisher:
Published: 1972
Total Pages: 361
ISBN-13:
DOWNLOAD EBOOKAuthor: Michael Reed
Publisher:
Published: 1972
Total Pages: 361
ISBN-13:
DOWNLOAD EBOOKAuthor: Michael Reed
Publisher:
Published: 1975
Total Pages: 361
ISBN-13:
DOWNLOAD EBOOKAuthor: Matteo Gallone
Publisher: Springer Nature
Published: 2023-04-04
Total Pages: 557
ISBN-13: 303110885X
DOWNLOAD EBOOKThis book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Author: M. W. Wong
Publisher: Springer Science & Business Media
Published: 2011-05-30
Total Pages: 175
ISBN-13: 3034801165
DOWNLOAD EBOOKThis textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.
Author: Michael Reed
Publisher: Gulf Professional Publishing
Published: 1980
Total Pages: 417
ISBN-13: 0125850506
DOWNLOAD EBOOK"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description.
Author: Michael Reed
Publisher:
Published: 1972
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Christopher D. Sogge
Publisher: Cambridge University Press
Published: 2017-04-27
Total Pages: 349
ISBN-13: 1107120071
DOWNLOAD EBOOKThis advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.
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Publisher:
Published: 1972
Total Pages:
ISBN-13:
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