Methods Of Spectral Analysis In Mathematical Physics PDF Download
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| Author | : Jan Janas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2008-12-16 |
| Genre | : Science |
| ISBN | : 3764387556 |
Download Methods of Spectral Analysis in Mathematical Physics Book in PDF, ePub and Kindle
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 |
| Publisher | : Birkhäuser |
| Total Pages | : 247 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034879474 |
Download Spectral Methods for Operators of Mathematical Physics Book in PDF, ePub and Kindle
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 | : Fedor S. Rofe-Beketov |
| Publisher | : World Scientific |
| Total Pages | : 466 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9812703454 |
Download Spectral Analysis of Differential Operators Book in PDF, ePub and Kindle
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 | : Yu.M. Berezansky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 983 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 940110509X |
Download Spectral Methods in Infinite-Dimensional Analysis Book in PDF, ePub and Kindle
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 | : I︠U︡riĭ Makarovich Berezanskiĭ |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 600 |
| Release | : 1994 |
| Genre | : Degree of freedom |
| ISBN | : 9780792328476 |
Download Spectral methods in infinite-dimensional analysis. 1 (1995) Book in PDF, ePub and Kindle
| Author | : Nobuaki Obata |
| Publisher | : Springer |
| Total Pages | : 141 |
| Release | : 2017-02-17 |
| Genre | : Science |
| ISBN | : 9811035067 |
Download Spectral Analysis of Growing Graphs Book in PDF, ePub and Kindle
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 | : Akihito Hora |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 384 |
| Release | : 2007-07-05 |
| Genre | : Science |
| ISBN | : 3540488634 |
Download Quantum Probability and Spectral Analysis of Graphs Book in PDF, ePub and Kindle
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 | : Bernard Shizgal |
| Publisher | : Springer |
| Total Pages | : 431 |
| Release | : 2015-01-07 |
| Genre | : Science |
| ISBN | : 9401794545 |
Download Spectral Methods in Chemistry and Physics Book in PDF, ePub and Kindle
This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.
| Author | : Lambert H. Koopmans |
| Publisher | : Elsevier |
| Total Pages | : 385 |
| Release | : 1995-05-18 |
| Genre | : Mathematics |
| ISBN | : 0080541569 |
Download The Spectral Analysis of Time Series Book in PDF, ePub and Kindle
To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results.The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications.Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. Hilbert spaces univariate models for spectral analysis multivariate spectral models sampling, aliasing, and discrete-time models real-time filtering digital filters linear filters distribution theory sampling properties of spectral estimates linear prediction
| Author | : Nathalie Sinclair |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2007-12-28 |
| Genre | : Mathematics |
| ISBN | : 0387381457 |
Download Mathematics and the Aesthetic Book in PDF, ePub and Kindle
This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
