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Author : Israel Gohberg,Mark Grigorʹevich Kreĭn
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 50,9 Mb
Release : 1978
Category : Mathematics
ISBN : 0821886509
Author : I. C. Gohberg,Mark Grigorʹevich Kreĭn
Publisher : Unknown
Page : 399 pages
File Size : 45,6 Mb
Release : 1969
Category : Hilbert space
ISBN : 1470444364
Author : Israel Gohberg,M. G. Krein
Publisher : Unknown
Page : 378 pages
File Size : 47,8 Mb
Release : 1969
Category : Hilbert space
ISBN : OCLC:318169320
Author : Yiśrāʿēl Z. Gohberg,Mark G. Krejn
Publisher : Unknown
Page : 0 pages
File Size : 49,6 Mb
Release : 1969
Category : Electronic
ISBN : OCLC:1070392899
Author : John Locker
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 44,6 Mb
Release : 2000
Category : Nonselfadjoint operators
ISBN : 9780821820490
Develops the spectral theory of an nth order non-self-adjoint two- point differential operator L in the complex Hilbert space L2[0,1]. The differential operator L is determined by an nth order formal differential l and by n linearly independent boundary values B1,.,Bn. Locker first lays the foundations of the spectral theory for closed linear operators and Fredholm operators in Hilbert spaces before developing the spectral theory of the differential operator L. The book is a sequel to Functional analysis and two-point differential operators, 1986. Annotation copyrighted by Book News, Inc., Portland, OR.
Author : Oktay Veliev
Publisher : Springer Nature
Page : 301 pages
File Size : 47,8 Mb
Release : 2021-06-19
Category : Science
ISBN : 9783030726836
This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
Author : Fabio Bagarello,Jean-Pierre Gazeau,Franciszek Hugon Szafraniec,Miloslav Znojil
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 51,9 Mb
Release : 2015-07-24
Category : Science
ISBN : 9781118855263
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
Author : Moshe S. Livsic,Leonid L. Waksman
Publisher : Springer
Page : 116 pages
File Size : 42,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478775
Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves.
Author : I. Gohberg,P. Lancaster,P.N. Shivakumar
Publisher : Birkhäuser
Page : 448 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890359
The papers selected for publication here, many of them written by leaders in the field, bring readers up to date on recent achievements in modern operator theory and applications. The book’s subject matter is of practical use to a wide audience in mathematical and engineering sciences.
Author : Michael A. Dritschel
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 53,8 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783764379803
This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functional analysis and its applications. The works are written by world authorities in their specialities.
Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257004
This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.
Author : Themistocles M. Rassias,Valentin A. Zagrebnov
Publisher : Springer
Page : 416 pages
File Size : 44,8 Mb
Release : 2019-05-31
Category : Mathematics
ISBN : 9783030126612
Dedicated to Tosio Kato’s 100th birthday, this book contains research and survey papers on a broad spectrum of methods, theories, and problems in mathematics and mathematical physics. Survey papers and in-depth technical papers emphasize linear and nonlinear analysis, operator theory, partial differential equations, and functional analysis including nonlinear evolution equations, the Korteweg–de Vries equation, the Navier–Stokes equation, and perturbation theory of linear operators. The Kato inequality, the Kato type matrix limit theorem, the Howland–Kato commutator problem, the Kato-class of potentials, and the Trotter–Kato product formulae are discussed and analyzed. Graduate students, research mathematicians, and applied scientists will find that this book provides comprehensive insight into the significance of Tosio Kato’s impact to research in analysis and operator theory.
Author : Michael Demuth,Werner Kirsch
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 40,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9783034805919
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 : Alexander G. Ramm,P. N. Shivakumar,Abraham Vilgelmovich Strauss
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 49,9 Mb
Release : 2000
Category : Operator theory
ISBN : 9780821819906
Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.
Author : Jonathan R. Partington
Publisher : Cambridge University Press
Page : 116 pages
File Size : 49,6 Mb
Release : 1988
Category : Mathematics
ISBN : 0521367913
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.