Download or read book Topics in Interpolation Theory written by Bernd Fritzsche and published by Birkhäuser. This book was released on 2012-12-06 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: About one half of the papers in this volume are based on lectures which were pre sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).
Download or read book Topics In Interpolation Theory written by Harry Dym and published by Springer Science & Business Media. This book was released on 1997 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.
Download or read book Interpolation Theory written by Alessandra Lunardi and published by Springer. This book was released on 2018-05-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Download or read book Interpolation Theory Systems Theory and Related Topics written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Download or read book Function Spaces Interpolation Theory and Related Topics written by Michael Cwikel and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Interpolation and Approximation written by Philip J. Davis and published by Courier Corporation. This book was released on 1975-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
Download or read book Topics in Interpolation Theory of Rational Matrix valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.
Download or read book Interpolation Spaces and Allied Topics in Analysis written by M. Cwikel and published by Springer. This book was released on 2006-12-08 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frontiers in Interpolation and Approximation written by N. K. Govil and published by CRC Press. This book was released on 2006-07-20 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.
Download or read book Interpolation and Approximation by Polynomials written by George M. Phillips and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Download or read book Interpolation Theory Systems Theory and Related Topics written by Harry Dym and published by Birkhauser. This book was released on 2002-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpolation Theory and Applications written by Michael Cwikel and published by American Mathematical Soc.. This book was released on 2007 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.
Download or read book Topics in Interpolation Theory of Rational Matrix valued Functions written by Israel Gohberg and published by . This book was released on 1988 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interpolation Processes written by Giuseppe Mastroianni and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vértesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses,usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness,K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.
Download or read book Advanced Topics in Shannon Sampling and Interpolation Theory written by Robert J.II Marks and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling theory will make this an invaluable research tool as well as an excellent text for students planning further research in the field.
Download or read book Operator Theory and Interpolation written by Hari Bercovic and published by Birkhäuser. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.
Download or read book Interpolation of Functions written by J. Szabados and published by World Scientific. This book was released on 1990 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics.
