Progress In Approximation Theory

Author : Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser
Publisher : Springer
Page : 519 pages
File Size : 55,9 Mb
Release : 2017-04-03
Category : Mathematics
ISBN : 9783319492421

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Progress in Approximation Theory and Applicable Complex Analysis by Narendra Kumar Govil,Ram Mohapatra,Mohammed A. Qazi,Gerhard Schmeisser Pdf

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.

Author : A.A. Gonchar,E.B. Saff
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229667

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Progress in Approximation Theory by A.A. Gonchar,E.B. Saff Pdf

Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.

Author : Paul G. Nevai,Allan Pinkus
Publisher : Unknown
Page : 936 pages
File Size : 47,8 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015009126585

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Progress in Approximation Theory by Paul G. Nevai,Allan Pinkus Pdf

Author : A. A. Gonchar,E. B. Saff
Publisher : Unknown
Page : 476 pages
File Size : 50,5 Mb
Release : 1992-11-01
Category : Electronic
ISBN : 1461229677

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Progress in Approximation Theory by A. A. Gonchar,E. B. Saff Pdf

Author : A.A. Gonchar,E.B. Saff
Publisher : Springer
Page : 451 pages
File Size : 49,5 Mb
Release : 1992-11-12
Category : Mathematics
ISBN : 0387979018

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Progress in Approximation Theory by A.A. Gonchar,E.B. Saff Pdf

Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.

Author : N. I. Achieser
Publisher : Courier Corporation
Page : 324 pages
File Size : 52,5 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780486153131

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Theory of Approximation by N. I. Achieser Pdf

A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).

Author : S. A. Mohiuddine,Tuncer Acar
Publisher : Springer
Page : 241 pages
File Size : 50,9 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9789811330773

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Advances in Summability and Approximation Theory by S. A. Mohiuddine,Tuncer Acar Pdf

This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.

Author : George A. Anastassiou,Oktay Duman
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 53,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781461463931

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Advances in Applied Mathematics and Approximation Theory by George A. Anastassiou,Oktay Duman Pdf

Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.​

Author : Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal
Publisher : Springer
Page : 304 pages
File Size : 48,7 Mb
Release : 2019-08
Category : Electronic
ISBN : 3030063747

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Recent Advances in Constructive Approximation Theory by Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal Pdf

This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type convergence of GBS operators.

Author : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 45,5 Mb
Release : 2007-07-28
Category : Mathematics
ISBN : 9780817644758

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The History of Approximation Theory by Karl-Georg Steffens Pdf

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

Author : Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados
Publisher : CRC Press
Page : 560 pages
File Size : 45,5 Mb
Release : 1998-05-12
Category : Mathematics
ISBN : 0824701852

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Approximation Theory by Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados Pdf

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Author : Feng Dai,Yuan Xu
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 49,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461466604

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Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai,Yuan Xu Pdf

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Author : Javad Mashreghi,Myrto Manolaki,Paul Gauthier
Publisher : Springer
Page : 278 pages
File Size : 54,7 Mb
Release : 2018-03-28
Category : Mathematics
ISBN : 9781493975433

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New Trends in Approximation Theory by Javad Mashreghi,Myrto Manolaki,Paul Gauthier Pdf

The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

Author : Hrushikesh Narhar Mhaskar,Devidas V. Pai
Publisher : Alpha Science International, Limited
Page : 572 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : UCSC:32106019292199

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Fundamentals of Approximation Theory by Hrushikesh Narhar Mhaskar,Devidas V. Pai Pdf

This book presents a systematic and in-depth treatment of some basic topics in approximation theory in an effort to emphasize the rich connections of different branches of analysis with this subject. It contains a good blend of both the classical as well as abstract topics in the domain and their interconnections as appropriate. The approach is from the very concrete to more and more abstract levels. In order to provide a historical perspective on the results, a section on notes is appended to each chapter with an extensive bibliography. Researchers will find several references to recent developments. Problems of varying degree of difficulty accompany each chapter. Some of these problems complement certain results from the text. The others, more challenging, are drawn from the contemporary research articles. Ample hints are provided for such problems. Primarily aimed at graduate students and teachers of mathematics, researchers interested in an introduction to the specific results or techniques of approximation theory will find this book very attractive.

Author : Werner Haussmann,Kurt Jetter,Manfred Reimer
Publisher : Birkhäuser
Page : 258 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882729

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Recent Progress in Multivariate Approximation by Werner Haussmann,Kurt Jetter,Manfred Reimer Pdf

Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.