The Commutant Lifting Approach To Interpolation Problems
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The Commutant Lifting Approach To Interpolation Problems
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Author : Foias
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
The Commutant Lifting Approach To Interpolation Problems written by Foias and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Social Science categories.
Classical H interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Mobius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R. G. Douglas, P. S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L to H . At about the sametime as Sarason's work, V. M."
Operator Theory And Boundary Eigenvalue Problems
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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Theory And Boundary Eigenvalue Problems written by I. 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.
The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.
Holomorphic Spaces
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Author : Sheldon Jay Axler
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-28
Holomorphic Spaces written by Sheldon Jay Axler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-28 with Mathematics categories.
Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
Spectral Theory Of Approximation Methods For Convolution Equations
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Author : Roland Hagen
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Spectral Theory Of Approximation Methods For Convolution Equations written by Roland Hagen 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.
The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.
Floquet Theory For Partial Differential Equations
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Author : P.A. Kuchment
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Floquet Theory For Partial Differential Equations written by P.A. Kuchment 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 Social Science categories.
Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].
Well Posedness Of Parabolic Difference Equations
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Author : A. Ashyralyev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Well Posedness Of Parabolic Difference Equations written by A. Ashyralyev 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.
A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Differentiable Operators And Nonlinear Equations
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Author : Victor Khatskevich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Differentiable Operators And Nonlinear Equations written by Victor Khatskevich 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.
The need to study holomorphic mappings in infinite dimensional spaces, in all likelihood, arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods, which subsequently have been refined and developed. Parallel with these achievements, the theory of functions of one or several complex variables was gradually enriched with more significant and subtle results. The present book is a first step towards establishing a bridge between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. The work concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting. In order to make this book accessible not only to specialists but also to students and engineers, the authors give a complete account of definitions and proofs, and also present relevant prerequisites from functional analysis and topology. Contents: Preliminaries • Differential calculus in normed spaces • Integration in normed spaces • Holomorphic (analytic) operators and vector-functions on complex Banach spaces • Linear operators • Nonlinear equations with differentiable operators • Nonlinear equations with holomorphic operators • Banach manifolds • Non-regular solutions of nonlinear equations • Operators on spaces with indefinite metric • References • List of Symbols • Subject Index.
Classes Of Linear Operators
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Author : Israel Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2013-03-09
Classes Of Linear Operators 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 2013-03-09 with Social Science categories.
These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.
Operator Theory And Complex Analysis
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Author : T. Ando
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Theory And Complex Analysis written by T. Ando 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 Social Science categories.
Mathematical Methods In Systems Optimization And Control
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Author : Harry Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25
Mathematical Methods In Systems Optimization And Control written by Harry Dym 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 2012-07-25 with Mathematics categories.
This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.