Equations With Involutive Operators
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Equations With Involutive Operators
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Author : Nikolai Karapetiants
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-21
Equations With Involutive Operators written by Nikolai Karapetiants 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 2001-06-21 with Mathematics categories.
This self-contained title demonstrates an important interplay between abstract and concrete operator theory. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the-art topics. Good examples, bibliography and index make this text a valuable classroom or reference resource.
Equations With Involutive Operators
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Author : Nikolai Karapetiants
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Equations With Involutive Operators written by Nikolai Karapetiants 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.
"Equations with Involutive Operators" demonstrates an important interplay between abstract and concrete operator theory. The focus is on the investigation of a number of equations, which, while seemingly different, are all unified by the same idea: they are all realizations of some operator equations in Banach spaces. One permeating theme in these equations involves the role of the Fredholm property. The text is carefully written, self-contained, and covers a broad range of topics and results. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the art topics. Experts in operator theory, integral equations, and function theory as well as students in these areas will find open problems for further investigations. The book will also be useful to engineers using operator theory and integral equation techniques. Good examples, bibliography and index make this text a valuable classroom or reference resource.
Approximation Of Additive Convolution Like Operators
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Author : Victor Didenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-19
Approximation Of Additive Convolution Like Operators written by Victor Didenko 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 2008-09-19 with Mathematics categories.
This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.
Limit Operators And Their Applications In Operator Theory
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Author : Vladimir Rabinovich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Limit Operators And Their Applications In Operator Theory written by Vladimir Rabinovich and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This text has two goals. It describes a topic: band and band-dominated operators and their Fredholm theory, and it introduces a method to study this topic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+ Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of [2(Z) is the family of sequences (ei)iEZ where ei = (. . . ,0,0, 1,0,0, . . . ) with the 1 standing at the ith place. Every bounded linear operator A on H can be described by a two-sided infinite matrix (aij)i,jEZ with respect to this basis, where aij = (Aej, ei)' The band operators on H are just the operators with a matrix representation of finite band-width, i. e. , the operators for which aij = 0 whenever Ii - jl > k for some k. Operators which are in the norm closure ofthe algebra of all band operators are called band-dominated. Needless to say that band and band dominated operators appear in numerous branches of mathematics. Archetypal examples come from discretizations of partial differential operators. It is easy to check that every band operator can be uniquely written as a finite sum L dkVk where the d are multiplication operators (i. e.
Advances In Harmonic Analysis And Operator Theory
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Author : Alexandre Almeida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-31
Advances In Harmonic Analysis And Operator Theory written by Alexandre Almeida 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 2013-01-31 with Mathematics categories.
This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.
Operator Algebras Operator Theory And Applications
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Author : Maria Amélia Bastos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-27
Operator Algebras Operator Theory And Applications written by Maria Amélia Bastos 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 2008-05-27 with Mathematics categories.
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Operator Theoretical Methods And Applications To Mathematical Physics
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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Theoretical Methods And Applications To Mathematical Physics written by Israel Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag). Moreover he played a decisive role in the foundation of these two series by helping to establish contacts between Birkhauser and the founder and present chief editor of this book series after his emigration from Moldavia in 1974. The volume is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to E. Meister. We hope that a great part of the numerous features of his life and work can be re-discovered from this book.
Modern Methods In Operator Theory And Harmonic Analysis
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Author : Alexey Karapetyants
language : en
Publisher: Springer Nature
Release Date : 2019-08-28
Modern Methods In Operator Theory And Harmonic Analysis written by Alexey Karapetyants and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-28 with Mathematics categories.
This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.
Operator Theory And Harmonic Analysis
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Author : Alexey N. Karapetyants
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Operator Theory And Harmonic Analysis written by Alexey N. Karapetyants and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.
Functional Differential Equations
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Author : A. B. Antonevich
language : en
Publisher: CRC Press
Release Date : 1998-08-15
Functional Differential Equations written by A. B. Antonevich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-15 with Mathematics categories.
Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of Volume II contain the applications of the C*-structures and theory developed in Volume I. They show the technique of using the C*-results in the study of the solvability conditions of non-local functional differential equations and demonstrate the fundamental principles underlying the interrelations between C* and functional differential objects. The authors focus on non-local pseudodifferential, singular integral, and Toeplitz operators-with continuous and piecewise continuous coefficients-convolution type operators with oscillating coefficients and shifts, and operators associated with non-local boundary value problems containing transformation operators of an argument on the boundary. They build the symbolic calculus for all these classes of operators, use it to treat concrete examples of non-local operators, present the explicit computation of their Fredholmity conditions and the index formulae, and obtain a number of related results. Part 1: Equations with Continuous Coefficients and Part 2: Equations with Discontinuous Coefficients and Boundary Value Problems can each stand alone and prove a valuable resource for researchers and students interested in operator algebraic methods in the theory of functional differential equations, and to pure C*-algebraists looking for important and promising new applications. Together these books form a powerful library for this intriguing field of modern analysis.