Analysis Of Spectral Charactristics Of One Nonself Adjoint Problem
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Spectral Properties Of Non Self Adjoint Operators
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Author : John L. Weir
language : en
Publisher:
Release Date : 2010
Spectral Properties Of Non Self Adjoint Operators written by John L. Weir and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Nonselfadjoint operators categories.
The aim of this thesis is to study the spectral properties of non-self-adjoint operators via related self-adjoint operators. We consider two different prob-lems: one in which the spectra of a family of non-self-adjoint operators are identical to those of a family of self-adjoint operators and one in which the growth rates of semigroups generated by non-self-adjoint operators are bounded by the growth rates of semigroups generated by related self-adjoint operators. -- In the first problem, we consider a family of non-self-adjoint operators arising in the study of a problem in fluid mechanics in a paper written by Benilov, O'Brien and Sazonov, who argued from numerical and asymptotic evidence that the spectra of the operators are real. We show that the spectra of the operators are identical to the spectra of a family of self-adjoint operators and consist of infinitely many real eigenvalues which accumulate only at infinity. We make use of this correspondence to study certain other properties of the eigenvalues of the non-self-adjoint operators via the self-adjoint operators. In particular, we consider the asymptotic distribution of the eigenvalues for each fixed operator, and the behaviour of each eigenvalue as a small parameter tends to zero. -- In the second, we study the spectral asymptotics of large skew symmetric perturbations of a wide class of Schrodinger operators, generalizing some of the results obtained by Gallagher, Gallay and Nier for the one-dimensional quantum harmonic oscillator. We obtain bounds on the growth rates of the one-parameter semigroups generated by the perturbed operators in terms of the minima of the spectra of related self-adjoint operators. These self-adjoint operators are perturbations of the original Schrodinger operators by non-negative potentials, and we obtain lower bounds on the spectral minima in terms of the behaviour of the potentials at their zeros.
Analysis Of Spectral Charactristics Of One Nonself Adjoint Problem
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Author : Karwan Jwamer
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-10
Analysis Of Spectral Charactristics Of One Nonself Adjoint Problem written by Karwan Jwamer and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10 with categories.
This book is devoted to study of asymptotic behavior of eigenvalues and eigenfunctions of one nonself-adjoint boundary value problem with nonsmooth coefficients, receipt of upper bounds of normalized eigenfunctions in case of summable weight function and establishment of the greatest possible growth rate of eigenfunctions in the considered problem in case of various weight functions. It has been proved that in case of the weight function satisfying Lipschitz condition (in a regular case), normalized eigenfunctions of the problem are uniformly bounded. The results of this book can be used in solution of various problems in mechanics, theory of elasticity, mathematical physics, and optimal control because, as is known, spectral boundary value problems simulate many applications. Can also find their use in mathematics in vindication of Fourier method, in study of convergence of various expansions, etc. This book should be useful in courses on spectral boundary value problems, and generalized problem of evaluation of eigenfunctions in nonself-adjoint boundary value problems.
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 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.
Quaternionic De Branges Spaces And Characteristic Operator Function
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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2020-01-27
Quaternionic De Branges Spaces And Characteristic Operator Function written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-27 with Mathematics categories.
This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
Method Of Spectral Mappings In The Inverse Problem Theory
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Author : Vacheslav A. Yurko
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-10
Method Of Spectral Mappings In The Inverse Problem Theory written by Vacheslav A. Yurko and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-10 with Mathematics categories.
Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.
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.
Hamiltonian Methods In The Theory Of Solitons
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Author : Ludwig Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-10
Hamiltonian Methods In The Theory Of Solitons written by Ludwig Faddeev 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 2007-08-10 with Science categories.
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
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 Expansions Of Non Self Adjoint Generalized Laguerre Semigroups
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Author : Pierre Patie
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-16
Spectral Expansions Of Non Self Adjoint Generalized Laguerre Semigroups written by Pierre Patie and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.
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