Spectral Methods For Operators Of Mathematical Physics
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Spectral Methods For Operators Of Mathematical Physics
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Author : Jan Janas
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Spectral Methods For Operators Of Mathematical Physics written by Jan Janas and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Spectral Methods In Infinite Dimensional Analysis 2 1995
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Author : I︠U︡riĭ Makarovich Berezanskiĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Spectral Methods In Infinite Dimensional Analysis 2 1995 written by I︠U︡riĭ Makarovich Berezanskiĭ 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 1995 with Degree of freedom categories.
Spectral Methods In Infinite Dimensional Analysis
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Author : Yu.M. Berezansky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Spectral Methods In Infinite Dimensional Analysis written by Yu.M. Berezansky 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 2013-06-29 with Mathematics categories.
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.
Spectral Methods In Soliton Equations
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Author : I D Iliev
language : en
Publisher: CRC Press
Release Date : 1994-11-21
Spectral Methods In Soliton Equations written by I D Iliev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-21 with Mathematics categories.
Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.
Operators Geometry And Quanta
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Author : Dmitri Fursaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-25
Operators Geometry And Quanta written by Dmitri Fursaev 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 2011-06-25 with Science categories.
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Methods Of Spectral Analysis In Mathematical Physics
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Author : Jan Janas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-16
Methods Of Spectral Analysis In Mathematical Physics written by Jan Janas 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 2008-12-16 with Science categories.
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.
Spectral Methods
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Author : Claudio Canuto
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-23
Spectral Methods written by Claudio Canuto 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 2007-09-23 with Science categories.
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Spectral Analysis Of Differential Operators
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Author : Fedor S. Rofe-Beketov
language : en
Publisher: World Scientific
Release Date : 2005
Spectral Analysis Of Differential Operators written by Fedor S. Rofe-Beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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."
Spectral Theory Of Block Operator Matrices And Applications
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Author : Christiane Tretter
language : en
Publisher: World Scientific
Release Date : 2008-10-15
Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-15 with Science categories.
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics. The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics. Contents:Bounded Block Operator Matrices:The Quadratic Numerical RangeSpecial Classes of Block Operator MatricesSpectral InclusionEstimates of the ResolventCorners of the Quadratic Numerical RangeSchur Complements and Their FactorizationBlock DiagonalizationSpectral Supporting SubspacesVariational Principles for Eigenvalues in GapsJ-Self-Adjoint Block Operator MatricesThe Block Numerical RangeNumerical Ranges of Operator PolynomialsGershgorin's Theorem for Block Operator MatricesUnbounded Block Operator Matrices:Relative Boundedness and Relative CompactnessClosedness and Closability of Block Operator MatricesSpectrum and ResolventThe Essential SpectrumSpectral InclusionSymmetric and J-Symmetric Block Operator MatricesDichotomous Block Operator Matrices and Riccati EquationsBlock Diagonalization and Half Range CompletenessUniqueness Results for Solutions of Riccati EquationsVariational PrinciplesEigenvalue EstimatesApplications in Mathematical Physics:Upper Dominant Block Operator Matrices in MagnetohydrodynamicsDiagonally Dominant Block Operator Matrices in Fluid MechanicsOff-Diagonally Dominant Block Operator Matrices in Quantum Mechanics Readership: Mathematicians, physicists and engineers. Keywords:Operator Theory;Spectral Theory;Eigenvalues;Differential Equations;Riccati Equations;Numerical Range;Mathematical Physics;Matrix TheoryKey Features:Challenging spectral problems to which standard methods do not applyNew results even in the finite dimensional caseMany illustrating examplesWide range of possible applicationsReviews:“This book is a valuable addition to the literature and will be of great help for those working in this field already as well as for people looking for an interesting introduction to the topic.”Mathematical Reviews
Spectral Operator Theory And Related Topics
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Author : Vladimir Aleksandrovich Marchenko
language : en
Publisher:
Release Date : 1994
Spectral Operator Theory And Related Topics written by Vladimir Aleksandrovich Marchenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
This collection contains papers by participants in the Seminar on Mathematical Physics in Kharkov, Ukraine. The papers mainly focus on nontraditional problems of spectral theory, such as new types of inverse problems for one-dimensional differential operators, new classes of solutions to nonlinear differential equations obtained using spectral methods, distribution of eigenvalues of large random matrices, and related problems of statistical physics of disordered systems. In addition, the papers explore the spectral aspects of homogenization and of properties of ergodic dynamical systems. All t.