A Collection Of Problems In Spectral Analysis For Self Adjoint And Non Self Adjoint Operators
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A Collection Of Problems In Spectral Analysis For Self Adjoint And Non Self Adjoint Operators
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Author : Francesco Ferrulli
language : en
Publisher:
Release Date : 2019
A Collection Of Problems In Spectral Analysis For Self Adjoint And Non Self Adjoint Operators written by Francesco Ferrulli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Spectral Analysis Of Differential Operators Interplay Between Spectral And Oscillatory Properties
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Author : Fedor S Rofe-beketov
language : en
Publisher: World Scientific
Release Date : 2005-08-29
Spectral Analysis Of Differential Operators Interplay Between Spectral And Oscillatory Properties 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 2005-08-29 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 Schrödinger 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 Self Adjoint Operators In Hilbert Space
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Author : Michael Sh. Birman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Self Adjoint Operators In Hilbert Space written by Michael Sh. Birman 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 2012-12-06 with Mathematics categories.
It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Spectral Analysis Of Non Self Adjoint Operators And Intermediate Systems
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Author : Mikhail Samoĭlovich Brodskiĭ
language : en
Publisher:
Release Date : 1960
Spectral Analysis Of Non Self Adjoint Operators And Intermediate Systems written by Mikhail Samoĭlovich Brodskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations
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Author : Johannes Sjöstrand
language : en
Publisher: Springer
Release Date : 2019-05-17
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations written by Johannes Sjöstrand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Mathematics categories.
The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Commuting Nonselfadjoint Operators In Hilbert Space
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Author : Moshe S. Livsic
language : en
Publisher: Springer
Release Date : 2006-11-15
Commuting Nonselfadjoint Operators In Hilbert Space written by Moshe S. Livsic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Non Selfadjoint Operators In Quantum Physics
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Author : Fabio Bagarello
language : en
Publisher: John Wiley & Sons
Release Date : 2015-07-24
Non Selfadjoint Operators In Quantum Physics written by Fabio Bagarello and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-24 with Science categories.
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.
Problems Of The Spectral Theory Of Non Self Adjoint Operators
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Author : M. V. Keldysh
language : en
Publisher:
Release Date : 1972
Problems Of The Spectral Theory Of Non Self Adjoint Operators written by M. V. Keldysh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
The class of non self adjoint operators, for which the unconditionally converging expansion of the eigenfunctions is correct, has not yet been fully defined (for example, it is not known whether ellipital differential operators with partial derivatives belong to this class). However, it is now clear that the spectral expansion converging on the norm is not a necessary characteristic of the general linear operator. Apparently, further development of the theory will be achieved by establishing the generalized spectral expansion. It is noted that considerable material has been accumulated in the theory of non self adjoint problems, and it is characteristic that in recent years the theory has been supplemented with a number of new and important studies. Successes have been particularly great in the area of operators with discrete spectrum. The first three sections discuss this theme. (Author).
Spectral Theory Of Families Of Self Adjoint Operators
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Author : Anatolii M. Samoilenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Families Of Self Adjoint Operators written by Anatolii M. Samoilenko 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 2012-12-06 with Mathematics categories.
Spectral Theory Of Operators In Hilbert Space
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Author : Kurt O. Friedrichs
language : en
Publisher:
Release Date : 2014-09-01
Spectral Theory Of Operators In Hilbert Space written by Kurt O. Friedrichs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.