Methods Of Spectral Analysis In Mathematical Physics

Author : Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko,Günter Stolz
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 43,9 Mb
Release : 2008-12-16
Category : Science
ISBN : 9783764387556

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Methods of Spectral Analysis in Mathematical Physics by Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko,Günter Stolz Pdf

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Author : Jan Janas,Pavel Kurasov,Sergei Naboko
Publisher : Birkhäuser
Page : 247 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034879477

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Spectral Methods for Operators of Mathematical Physics by Jan Janas,Pavel Kurasov,Sergei Naboko Pdf

This book presents recent results in the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Author : I︠U︡riĭ Makarovich Berezanskiĭ,I︠U︡riĭ Grigorʹevich Kondratʹev
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 45,5 Mb
Release : 1994
Category : Degree of freedom
ISBN : 0792328477

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Spectral methods in infinite-dimensional analysis. 1 (1995) by I︠U︡riĭ Makarovich Berezanskiĭ,I︠U︡riĭ Grigorʹevich Kondratʹev Pdf

Author : Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic
Publisher : World Scientific
Page : 466 pages
File Size : 50,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703453

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Spectral Analysis of Differential Operators by Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic Pdf

This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."

Author : Akihito Hora,Nobuaki Obata
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 41,8 Mb
Release : 2007-07-05
Category : Science
ISBN : 9783540488637

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Quantum Probability and Spectral Analysis of Graphs by Akihito Hora,Nobuaki Obata Pdf

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Author : Yu.M. Berezansky,Y.G. Kondratiev
Publisher : Springer Science & Business Media
Page : 983 pages
File Size : 53,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401105095

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Spectral Methods in Infinite-Dimensional Analysis by Yu.M. Berezansky,Y.G. Kondratiev Pdf

The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.

Author : Michael Reed,Barry Simon
Publisher : Elsevier
Page : 325 pages
File Size : 47,8 Mb
Release : 1978-05-26
Category : Mathematics
ISBN : 9780080570457

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IV: Analysis of Operators by Michael Reed,Barry Simon Pdf

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 : Bernard Helffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 44,6 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9781107032309

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Spectral Theory and Its Applications by Bernard Helffer Pdf

Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

Author : Klaus Kirsten
Publisher : CRC Press
Page : 397 pages
File Size : 41,5 Mb
Release : 2001-12-13
Category : Mathematics
ISBN : 9781420035469

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Spectral Functions in Mathematics and Physics by Klaus Kirsten Pdf

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

Author : Nobuaki Obata
Publisher : Springer
Page : 138 pages
File Size : 44,6 Mb
Release : 2017-02-17
Category : Science
ISBN : 9789811035067

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Spectral Analysis of Growing Graphs by Nobuaki Obata Pdf

This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.

Author : Donald B. Percival,Andrew T. Walden
Publisher : Cambridge University Press
Page : 616 pages
File Size : 50,6 Mb
Release : 1993-06-03
Category : Mathematics
ISBN : 0521435412

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Spectral Analysis for Physical Applications by Donald B. Percival,Andrew T. Walden Pdf

This book is an up-to-date introduction to univariate spectral analysis at the graduate level, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. Spectral analysis finds extensive application in the analysis of data arising in many of the physical sciences, ranging from electrical engineering and physics to geophysics and oceanography. A valuable feature of the text is that many examples are given showing the application of spectral analysis to real data sets. Special emphasis is placed on the multitaper technique, because of its practical success in handling spectra with intricate structure, and its power to handle data with or without spectral lines. The text contains a large number of exercises, together with an extensive bibliography.

Author : V. A. Yurko
Publisher : Unknown
Page : 316 pages
File Size : 41,8 Mb
Release : 2002
Category : Inverse problems (Differential equations)
ISBN : 3110631210

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Method of Spectral Mappings in the Inverse Problem Theory by V. A. Yurko Pdf

Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.

Author : Helge Holden,Barry Simon,Gerald Teschl
Publisher : American Mathematical Soc.
Page : 409 pages
File Size : 47,5 Mb
Release : 2013-07-08
Category : Mathematics
ISBN : 9780821875742

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Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday by Helge Holden,Barry Simon,Gerald Teschl Pdf

This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu

Author : M. Sh. Birman
Publisher : Springer Science & Business Media
Page : 118 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468475951

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Spectral Theory and Wave Processes by M. Sh. Birman Pdf

The articles in this collection are devoted to various problems in mathematical physics and mathematical analysis, primarily in the fields of spectral theory and the theory of wave processes. The collection is intended for mathematicians sPf>cializing in the fields of mathematical physics, functional analysis, and the theory of differential equations. In addition, it is of some interest to theoretical physicists. The first paper deals with a mixed boundary value problem for a system of elasticity equations, and considers fields in the neighborhood of various wave fronts. The method used permits an estimate of the errors in the Ben-Menahem approximate method. Paper 2 investigates operators in separable Hilbert space given by double integrals of a type defined at the beginning of the paper, and in which integration is understood as the limit of the integral sums of Riemann-stieltjes. In paper 3, the problem of calculation of elastic constants for a laminarly inhomogeneous semi-infinite medium is conSidered, and the uniqueness of the solution of the inverse seismic problem at finite depth proved. The fourth paper gives a detailed account of the results of an earlier paper by the same author, in which he generalized to the three-dimensional case the trace formulas obtained for the one-dimensional Schroedinger operator. Asymptotic estimates of the resolvent kernel and solutions of the scattering problem are given.

Author : Sergio Albeverio,Anindita Balslev,Ricardo Weder
Publisher : Springer Nature
Page : 316 pages
File Size : 41,7 Mb
Release : 2021-06-03
Category : Mathematics
ISBN : 9783030684907

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Schrödinger Operators, Spectral Analysis and Number Theory by Sergio Albeverio,Anindita Balslev,Ricardo Weder Pdf

This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.