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 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 Interpolation Theory written by Alessandra Lunardi and published by Springer. This book was released on 2018-05-05 with total page 199 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 Extrapolation Theory with Applications written by Björn Jawerth and published by American Mathematical Soc.. This book was released on 1991 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades, interpolation theory has become an established field with many interesting applications to classical and modern analysis. In this book, the authors develop a general theory of extrapolation spaces, which is a complement to the familiar theory of interpolation spaces. Their results allow an extension of the classical extrapolation theorem of Yano to scales of Banach spaces. They give applications to classical and modern analysis, including extreme forms of Sobolev imbedding theorems, rearranging inequalities for classical operators, and Nash-Moser implicit function theorems.
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 Spaces written by J. Bergh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.
Download or read book Interpolation Theory and Its Applications written by Lev A. Sakhnovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5], [8), [13)-[16], [26)-[30], [57]). In this book we use a method of operator identities for investigating interpo lation problems. Following the method of operator identities we formulate a general interpolation problem containing the classical interpolation problems (Nevanlinna Pick, Caratheodory, Schur, Humburger, Krein) as particular cases. We write down the abstract form of the Potapov inequality. By solving this inequality we give the description of the set of solutions of the general interpolation problem in the terms of the linear-fractional transformation. Then we apply the obtained general results to a number of classical and new interpolation problems. Some chapters of the book are dedicated to the application of the interpola tion theory results to several other problems (the extension problem, generalized stationary processes, spectral theory, nonlinear integrable equations, functions with operator arguments). 2. Now we shall proceed to a more detailed description of the book contents.
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 Interpolation of Operators written by Colin Bennett and published by Academic Press. This book was released on 1988-04-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Download or read book Interpolation Theory and Its Applications written by Lev A. Sakhnovich and published by . This book was released on 2014-01-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Birkhoff Interpolation written by G. G. Lorentz and published by Cambridge University Press. This book was released on 1984-12-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.
Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Download or read book Extrapolation Interpolation and Smoothing of Stationary Time Series with Engineering Applications written by Norbert Wiener and published by Martino Fine Books. This book was released on 2013-11 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2013 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This is the second book by Norbert Wiener on time series and communication engineering. While the first one, "Cybernetics," treated the subject from a general standpoint and was more philosophical than mathematical, the present volume is more technical than theoretical, and forms a kind of companion piece to the first. It is intended as a tool for engineers working in the field of electrical communication and related subjects. The book consists of an introduction, five chapters, and three appendices. After explaining the general outline of the problem in the introduction, the author gives in Chapter I a review of generalized harmonic analysis which is necessary for the understanding of the following chapters. Chapters II and III are devoted to the problems of prediction and filtering respectively. In Chapter IV there is given a brief account of the theory of multiple prediction, that is, the theory of prediction when we deal with more than one time series at the same time. Finally, in Chapter V there is given a short discussion on the application of similar methods to a problem of approximate differentiation.
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 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 Noncommutative Function Theoretic Operator Theory and Applications written by Joseph A. Ball and published by Cambridge University Press. This book was released on 2021-12-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Download or read book Operator Theory and Interpolation written by Hari Bercovici and published by Birkhauser. This book was released on 2000-01-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Systems and control theories use sophisticated operator theoretical methods. They also provide new ideas and problems in operator theory." "The articles in this volume originated from the IWOTA conference held at Indiana University, Bloomington, in June 1996. They represent most of the areas that were discussed at the workshop with some emphasis on modern interpolation theory, a topic which has seen much progress in recent years."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
