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Author : Michael Reed,Barry Simon
Publisher : Elsevier
Page : 388 pages
File Size : 49,7 Mb
Release : 1975
Category : Mathematics
ISBN : 0125850026
Band 2.
Author : Michael Reed,Barry Simon
Publisher : Unknown
Page : 361 pages
File Size : 41,8 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:490472759
Author : Michael Reed,Barry Simon
Publisher : Unknown
Page : 361 pages
File Size : 49,9 Mb
Release : 1972
Category : Electronic
ISBN : OCLC:490472759
Author : Michael Reed
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 1972
Category : Mathematical physics
ISBN : OCLC:872388977
Author : Matteo Gallone,Alessandro Michelangeli
Publisher : Springer Nature
Page : 557 pages
File Size : 47,9 Mb
Release : 2023-04-04
Category : Science
ISBN : 9783031108853
This 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 : Michael Reed,Barry Simon
Publisher : Gulf Professional Publishing
Page : 417 pages
File Size : 43,8 Mb
Release : 1980
Category : Functional analysis
ISBN : 9780125850506
"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 : M. W. Wong
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 42,8 Mb
Release : 2011-05-30
Category : Mathematics
ISBN : 9783034801164
This 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 : Anonim
Publisher : Unknown
Page : 558 pages
File Size : 41,7 Mb
Release : 1981
Category : Nuclear physics
ISBN : UCSD:31822017904590
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 49,8 Mb
Release : 2008-07-11
Category : Mathematics
ISBN : 9780817644420
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Author : American Mathematical Society
Publisher : Unknown
Page : 1414 pages
File Size : 41,8 Mb
Release : 1975
Category : Electronic journals
ISBN : UVA:X001416734
Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 48,7 Mb
Release : 2011-07-30
Category : Mathematics
ISBN : 9783764399924
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Author : Michael Reed,Barry Simon
Publisher : Elsevier
Page : 325 pages
File Size : 42,6 Mb
Release : 1978-05-26
Category : Mathematics
ISBN : 9780080570457
BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical Physics This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.
Author : Valery Serov
Publisher : Springer
Page : 0 pages
File Size : 49,8 Mb
Release : 2018-08-31
Category : Mathematics
ISBN : 3319879855
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.
Author : Anonim
Publisher : Unknown
Page : 848 pages
File Size : 41,6 Mb
Release : 1996
Category : Mathematics
ISBN : UCAL:B4334169
Author : P.D. Hislop,I.M. Sigal
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461207412
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
