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Norm Estimations For Operator Valued Functions And Their Applications

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Norm Estimations For Operator Valued Functions And Their Applications

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Author : Michael Gil
language : en
Publisher: CRC Press
Release Date : 1995-08-16

Norm Estimations For Operator Valued Functions And Their Applications written by Michael Gil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-16 with Mathematics categories.

Intended for specialists in functional analysis and stability theory, this work presents a systematic exposition of estimations for norms of operator-valued functions, and applies the estimates to spectrum perturbations of linear operators and stability theory. The author demonstrates his own approach to spectrum perturbations.

Norm Estimations For Operator Valued Functions And Their Applications

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Author : Michael Gil
language : en
Publisher: CRC Press
Release Date : 2021-06-30

Operator Functions And Operator Equations

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Author : Michael Gil'
language : en
Publisher: World Scientific
Release Date : 2017-09-08

Operator Functions And Operator Equations written by Michael Gil' and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-08 with Mathematics categories.

This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.

Spectral Theory Of Localized Resonances And Applications

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Author : Youjun Deng
language : en
Publisher: Springer Nature
Release Date : 2024-03-22

Spectral Theory Of Localized Resonances And Applications written by Youjun Deng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-22 with Mathematics categories.

This book is devoted to the spectral theory of localized resonances including surface plasmon/polariton resonances, atypical resonances, anomalous localized resonances and interior transmission resonances. Those resonance phenomena arise in different physical contexts, but share similar features. They form the fundamental basis for many cutting-edge technologies and applications including invisibility cloaking and super-resolution imaging. The book presents a systematic and comprehensive treatment on these resonance phenomena and the associated applications in a unified manner from a mathematical and spectral perspective, covering acoustic, electromagnetic and elastic wave scattering. The book can serve as a handy reference book for researchers in this field and it can also serve as a textbook or an inspiring source for postgraduate students who are interested in entering this field.

Operator Functions And Localization Of Spectra

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Author : Michael I. Gil
language : en
Publisher: Springer
Release Date : 2003-12-09

Operator Functions And Localization Of Spectra written by Michael I. Gil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Mathematics categories.

Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

Theory And Applications Of Differentiable Functions Of Several Variables

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Theory And Applications Of Differentiable Functions Of Several Variables written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This colletion is the fourteenth in an ongoing series on differentiable functions of several variables, presenting recent contributions to a line of research begun by Sobolev in 1950. The papers study various spaces of differentiable functions of several real variables in Euclidean space, their imbeddings, equivalent normings, weighted estimates of derivatives, and traces on sets. Several questions of approximation in function spaces on the line, on a hyperboloid, and on Lobachevsky space are studied. Investigations of bilinear approximations are applied to estimates of the singular numbers of integral operators and widths. The authors also examine the asymptotics of the spectrum of elliptic systems, as well as the Dirichlet variational problem for a degenerate elliptic operator. Finally, a block method of solving Laplace's equation for nonanalytic boundary conditions is developed.

Partial Integral Operators And Integro Differential Equations

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Author : Jurgen Appell
language : en
Publisher: CRC Press
Release Date : 2000-02-29

Partial Integral Operators And Integro Differential Equations written by Jurgen Appell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

Matrix Norms And Their Applications

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Author : G. Belitskii
language : en
Publisher: Birkhäuser
Release Date : 2013-03-08

Matrix Norms And Their Applications written by G. Belitskii and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Social Science categories.

CHAPTER 1 - OPERATORS IN FINITE-DIMENSIONAL NORMED SPACES 1 §l. Norms of vectors, linear functionals, and linear operators. 1 § 2. Survey of spectral theory 14 § 3. Spectral radius . 17 § 4. One-parameter groups and semigroups of operators. 25 Appendix. Conditioning in general computational problems 28 CHAPTER 2 - SPECTRAL PROPERTIES OF CONTRACTIONS 33 §l. Contractive operators and isometries. 33 §2. Stability theorems. 46 §3. One-parameter semigroups of contractions and groups of isometries. 48 § 4. The boundary spectrum of extremal contractions. 52 §5. Extreme points of the unit ball in the space of operators. 64 §6. Critical exponents. 66 §7. The apparatus of functions on graphs. 72 §8. Combinatorial and spectral properties of t -contractions . 81 00 §9. Combinatorial and spectral properties of 96 nonnegative matrices. §10. Finite Markov chains. 102 §ll. Nonnegative projectors. 108 VI CHAPTER 3 - OPERATOR NORMS . 113 §l. Ring norms on the algebra of operators in E 113 §2. Characterization of operator norms. 126 §3. Operator minorants. . . . . . 133 §4. Suprema of families of operator norms 141 §5. Ring cross-norms . . 150 §6. Orthogonally-invariant norms. 152 CHAPTER 4 - STUDY OF THE ORDER STRUCTURE ON THE SET OF RING NORMS . 157 §l. Maximal chains of ring norms. 157 §2. Generalized ring norms. 160 §3. The lattice of subalgebras of the algebra End(E) 166 § 4 • Characterization of automorphisms 179 201 Brief Comments on the Literature 205 References . .

Mathematical Analysis In Interdisciplinary Research

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Author : Ioannis N. Parasidis
language : en
Publisher: Springer Nature
Release Date : 2022-03-10

Mathematical Analysis In Interdisciplinary Research written by Ioannis N. Parasidis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Mathematics categories.

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Function Spaces Interpolation Theory And Related Topics

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Author : Michael Cwikel
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22

Function Spaces Interpolation Theory And Related Topics written by Michael Cwikel 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 2008-08-22 with Mathematics categories.

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

Norm Estimations For Operator Valued Functions And Their Applications

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