Progress In Approximation Theory And Applicable Complex Analysis

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Progress in Approximation Theory and Applicable Complex Analysis

Author : Narendra Kumar Govil
Publisher : Springer
ISBN 13 : 331949242X
Total Pages : 519 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Progress in Approximation Theory and Applicable Complex Analysis by : Narendra Kumar Govil

Download or read book Progress in Approximation Theory and Applicable Complex Analysis written by Narendra Kumar Govil and published by Springer. This book was released on 2017-04-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Advances in Constructive Approximation Theory

Author : Vijay Gupta
Publisher : Springer
ISBN 13 : 9783030063740
Total Pages : 304 pages
Book Rating : 4.0/5 (637 download)

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Book Synopsis Recent Advances in Constructive Approximation Theory by : Vijay Gupta

Download or read book Recent Advances in Constructive Approximation Theory written by Vijay Gupta and published by Springer. This book was released on 2019-08 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Progress in Approximation Theory

Author : A.A. Gonchar
Publisher : Springer Science & Business Media
ISBN 13 : 1461229669
Total Pages : 463 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Progress in Approximation Theory by : A.A. Gonchar

Download or read book Progress in Approximation Theory written by A.A. Gonchar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Author : Robert B. Gardner
Publisher : Elsevier
ISBN 13 : 0128119888
Total Pages : 442 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials by : Robert B. Gardner

Download or read book Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials written by Robert B. Gardner and published by Elsevier. This book was released on 2022-02-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions Contains exhaustive references with thousands of citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research

Approximation, Complex Analysis, and Potential Theory

Author : Norair Arakelian
Publisher : Springer Science & Business Media
ISBN 13 : 9401009791
Total Pages : 275 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Approximation, Complex Analysis, and Potential Theory by : Norair Arakelian

Download or read book Approximation, Complex Analysis, and Potential Theory written by Norair Arakelian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Advances in Summability and Approximation Theory

Author : S. A. Mohiuddine
Publisher : Springer
ISBN 13 : 9811330778
Total Pages : 241 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Advances in Summability and Approximation Theory by : S. A. Mohiuddine

Download or read book Advances in Summability and Approximation Theory written by S. A. Mohiuddine and published by Springer. This book was released on 2018-12-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Sinc Methods of Numerical Analysis

Author : Gerd Baumann
Publisher : Springer Nature
ISBN 13 : 303049716X
Total Pages : 411 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis New Sinc Methods of Numerical Analysis by : Gerd Baumann

Download or read book New Sinc Methods of Numerical Analysis written by Gerd Baumann and published by Springer Nature. This book was released on 2021-04-23 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Author : Robert B. Gardner
Publisher : Academic Press
ISBN 13 : 012812007X
Total Pages : 444 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials by : Robert B. Gardner

Download or read book Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials written by Robert B. Gardner and published by Academic Press. This book was released on 2022-02-10 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities for polynomials and their derivatives are very important in many areas of mathematics, as well as in other computational and applied sciences; in particular they play a fundamental role in approximation theory. Here, not only Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials, but also ones for trigonometric polynomials and related functions, are treated in an integrated and comprehensive style in different metrics, both on general classes of polynomials and on important restrictive classes of polynomials. Primarily for graduate and PhD students, this book is useful for any researchers exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Markov-Bernstein-type inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions, and entire functions of exponential type Contains exhaustive references with more than five hundred citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research

Progress in Approximation Theory

Author : Paul G. Nevai
Publisher :
ISBN 13 :
Total Pages : 936 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Progress in Approximation Theory by : Paul G. Nevai

Download or read book Progress in Approximation Theory written by Paul G. Nevai and published by . This book was released on 1991 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods of Fourier Analysis and Approximation Theory

Author : Michael Ruzhansky
Publisher : Birkhäuser
ISBN 13 : 331927466X
Total Pages : 258 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Methods of Fourier Analysis and Approximation Theory by : Michael Ruzhansky

Download or read book Methods of Fourier Analysis and Approximation Theory written by Michael Ruzhansky and published by Birkhäuser. This book was released on 2016-03-11 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Complex Analysis, Functional Analysis and Approximation Theory

Author : J. Mujica
Publisher : Elsevier
ISBN 13 : 9780080872360
Total Pages : 296 pages
Book Rating : 4.8/5 (723 download)

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Book Synopsis Complex Analysis, Functional Analysis and Approximation Theory by : J. Mujica

Download or read book Complex Analysis, Functional Analysis and Approximation Theory written by J. Mujica and published by Elsevier. This book was released on 1986-05-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains papers of research of expository nature, and is addressed to research workers and advanced graduate students in mathematics. Some of the papers are the written and expanded texts of lectures delivered at the conference, whereas others have been included by invitation.

Approximation and Computation in Science and Engineering

Author : Nicholas J. Daras
Publisher : Springer Nature
ISBN 13 : 3030841227
Total Pages : 934 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Approximation and Computation in Science and Engineering by : Nicholas J. Daras

Download or read book Approximation and Computation in Science and Engineering written by Nicholas J. Daras and published by Springer Nature. This book was released on 2022-05-05 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

Mathematical Analysis, Approximation Theory and Their Applications

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 3319312812
Total Pages : 741 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Mathematical Analysis, Approximation Theory and Their Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis, Approximation Theory and Their Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-03 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Approximation Theory

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 1461213606
Total Pages : 520 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Approximation Theory by : George A. Anastassiou

Download or read book Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Approximation Theory and Analytic Inequalities

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030606228
Total Pages : 546 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Approximation Theory and Analytic Inequalities by : Themistocles M. Rassias

Download or read book Approximation Theory and Analytic Inequalities written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-07-21 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Approximation Theory XIII: San Antonio 2010

Author : Marian Neamtu
Publisher : Springer Science & Business Media
ISBN 13 : 1461407729
Total Pages : 418 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Approximation Theory XIII: San Antonio 2010 by : Marian Neamtu

Download or read book Approximation Theory XIII: San Antonio 2010 written by Marian Neamtu and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.

New Trends in Approximation Theory

Author : Javad Mashreghi
Publisher : Springer
ISBN 13 : 1493975439
Total Pages : 278 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis New Trends in Approximation Theory by : Javad Mashreghi

Download or read book New Trends in Approximation Theory written by Javad Mashreghi and published by Springer. This book was released on 2018-03-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.