Spectral Analysis Of Relativistic Operators

Author : A. A. Balinsky,W. D. Evans
Publisher : World Scientific
Page : 200 pages
File Size : 54,6 Mb
Release : 2011
Category : Science
ISBN : 9781848162181

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Spectral Analysis of Relativistic Operators by A. A. Balinsky,W. D. Evans Pdf

Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.

Author : A A Balinsky,W D Evans
Publisher : World Scientific
Page : 200 pages
File Size : 55,6 Mb
Release : 2010-10-15
Category : Science
ISBN : 9781908978820

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Spectral Analysis of Relativistic Operators by A A Balinsky,W D Evans Pdf

Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar–Herbst and Brown–Ravenhall, which are semibounded under appropriate circumstances. This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992. Contents:PreliminariesOperatorsSpectraMiscellany Readership: Researchers and graduate students in mathematics and physics. Keywords:Spectral Analysis of Dirac;Pauli;Chandrasekhar-Herbst;Brown-Ravenhall Operators;Zero Modes of Pauli and Weyl-Dirac OperatorsKey Features:Provides a self-contained and comprehensive treatment of the spectral properties of various operators that take relativistic effects into accountNo competing book covering this subject matterContains an up-to-date account of topics of considerable current interest to mathematics and mathematical physics communitiesReviews:“In this very interesting book, the authors give a comprehensive presentation of the study of the spectral properties of various operators which take relativistic effects into account. This book provides historical remarks and comments on developments of the research on the topics discussed. This is very good and important, because it is often time-consuming to trace back previous developments, and because mathematics does not always develop in a logical order.”Mathematical Reviews

Author : Gabor Kunstatter,Jeffrey G Williams,D E Vincent
Publisher : World Scientific
Page : 390 pages
File Size : 42,6 Mb
Release : 1992-02-28
Category : Electronic
ISBN : 9789814554879

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General Relativity And Relativistic Astrophysics - Proceedings Of The 4th Canadian Conference by Gabor Kunstatter,Jeffrey G Williams,D E Vincent Pdf

This proceedings contains the talks delivered at plenary and parallel sessions by leading researchers in both classical and quantum general relativity and in astrophysics.

Author : Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko,Günter Stolz
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 52,5 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 : Christophe Cheverry,Nicolas Raymond
Publisher : Birkhäuser
Page : 0 pages
File Size : 40,5 Mb
Release : 2022-05-07
Category : Mathematics
ISBN : 3030674649

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A Guide to Spectral Theory by Christophe Cheverry,Nicolas Raymond Pdf

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Author : W.O. Amrein
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401003162

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Non-Relativistic Quantum Dynamics by W.O. Amrein Pdf

The bulk of known results in spectral and scattering theory for Schrodinger operators has been derived by time-independent (also called stationary) methods, which make extensive use of re solvent estimates and the spectral theorem. In very recent years there has been a partial shift of emphasis from the time-indepen dent to the time-dependent theory, due to the discovery of new, essentially time-dependent proofs of a fair number of the principal results such as asymptotic completeness, absence of singularly con tinuous spectrum and properties of scattering cross sections. These new time-dependent arguments are somewhat simpler than the station ary ones and at the same time considerably closer to physical in tuition, in that they are based on a rather detailed description of the time evolution of states in configUration space (whence the designation "geometric methods" used by some authors). It seemed interesting to me to present some of these new meth ods from a strictly time-dependent point of view, by considering as the basic mathematical object strongly continuous unitary one parameter groups and avoiding the spectral theorem completely. The present volume may be viewed as an essay in this spirit. It is an extended version of a course taught in 1979 at the University of Geneva to undergraduate students enrolled in mathematical physics.

Author : Anonim
Publisher : Unknown
Page : 744 pages
File Size : 54,9 Mb
Release : 1975
Category : Nuclear energy
ISBN : UOM:39015023546420

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Nuclear Science Abstracts by Anonim Pdf

Author : Michael Cwikel,Laura De Carli,Mario Milman
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 53,6 Mb
Release : 2007
Category : Interpolation
ISBN : 9780821842072

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Interpolation Theory and Applications by Michael Cwikel,Laura De Carli,Mario Milman Pdf

This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Author : Jan Janas,Pavel Kurasov,Sergei Naboko
Publisher : Birkhäuser
Page : 247 pages
File Size : 44,7 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 : Anonim
Publisher : Unknown
Page : 764 pages
File Size : 49,9 Mb
Release : 1974
Category : Nuclear energy
ISBN : RUTGERS:39030044058669

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Nuclear Science Abstracts by Anonim Pdf

Author : B. Malcolm Brown,Jan Lang,Ian G. Wood
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 55,5 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9783034802635

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Spectral Theory, Function Spaces and Inequalities by B. Malcolm Brown,Jan Lang,Ian G. Wood Pdf

This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Author : Helge Holden,Barry Simon,Gerald Teschl
Publisher : American Mathematical Soc.
Page : 409 pages
File Size : 42,6 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 : S. Kantorovitz
Publisher : Springer
Page : 184 pages
File Size : 55,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540386667

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Spectral Theory of Banach Space Operators by S. Kantorovitz Pdf

Author : Michael Demuth,Werner Kirsch
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 47,9 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9783034805919

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Mathematical Physics, Spectral Theory and Stochastic Analysis by Michael Demuth,Werner Kirsch Pdf

This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.

Author : Rafael Benguria,Eduardo Friedman,Marius Mantoiu
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 50,6 Mb
Release : 2012-06-30
Category : Mathematics
ISBN : 9783034804141

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Spectral Analysis of Quantum Hamiltonians by Rafael Benguria,Eduardo Friedman,Marius Mantoiu Pdf

This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.​