Download or read book Series of Faber Polynomials written by P.K. Suetin and published by CRC Press. This book was released on 1998-03-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents some important classical and modern results of the series of Faber polynomials and their applications. Interest in this subject has increased rapidly over the last decade, although the presentation of research has, until now, been confined mainly to journal articles. Applications include theory of functions of complex variables, theory of analytic function approximation, and some aspects of numerical analysis.
Download or read book A Generalization of Faber s Polynomials written by Joseph Leonard Walsh and published by . This book was released on 1958 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer. This book was released on 2013-12-20 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Walsh Equiconvergence of Complex Interpolating Polynomials written by Amnon Jakimovski and published by Springer Science & Business Media. This book was released on 2007-05-16 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc. This book will be particularly useful for researchers in approximation and interpolation theory.
Download or read book Polynomials Orthogonal over a Region and Bieberbach Polynomials written by Pavel Kondratʹevich Suetin and published by American Mathematical Soc.. This book was released on 1974 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses orthogonal polynomials.
Download or read book Polynomial expansions of analytic functions written by Ralph P. Boas and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.
Download or read book Functional Analysis I written by Yu.I. Lyubich and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.
Download or read book Introduction to Functions of a Complex Variable written by J. H. Curtiss and published by CRC Press. This book was released on 2021-07-28 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes information on elementary general topology, the Cauchy Integral Theorem and concepts of homology and homotopy in their application to the Cauchy theory. It is intended for an introductory course in complex analysis at the first-year graduate and advanced undergraduate level.
Download or read book STUDIES IN FABER POLYNOMIALS written by HASSOON SHAKER AMIRI and published by . This book was released on 1961 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Menahem Max Schiffer Selected Papers Volume 1 written by Peter Duren and published by Springer Science & Business Media. This book was released on 2013-10-17 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set presents over 50 of the most groundbreaking contributions of Menahem M Schiffer. All of the reprints of Schiffer’s works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's work. A complete bibliography and brief biography make this a rounded and invaluable reference.
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.
Download or read book Polynomial Expansions of Analytic Functions written by Ralph P.Jr. Boas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.
Download or read book Overconvergence in Complex Approximation written by Sorin G. Gal and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the quantitative overconvergence phenomenon in complex approximation by various operators. The book is divided into three chapters. First, the results for the Schurer-Faber operator, Beta operators of first kind, Bernstein-Durrmeyer-type operators and Lorentz operator are presented. The main focus is on results for several q-Bernstein kind of operators with q > 1, when the geometric order of approximation 1/qn is obtained not only in complex compact disks but also in quaternion compact disks and in other compact subsets of the complex plane. The focus then shifts to quantitative overconvergence and convolution overconvergence results for the complex potentials generated by the Beta and Gamma Euler's functions. Finally quantitative overconvergence results for the most classical orthogonal expansions (of Chebyshev, Legendre, Hermite, Laguerre and Gegenbauer kinds) attached to vector-valued functions are presented. Each chapter concludes with a notes and open problems section, thus providing stimulation for further research. An extensive bibliography and index complete the text. This book is suitable for researchers and graduate students working in complex approximation and its applications, mathematical analysis and numerical analysis.
Download or read book Quaternionic Approximation written by Sorin G. Gal and published by Springer. This book was released on 2019-04-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable. The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.
Download or read book Exploiting Symmetry in Applied and Numerical Analysis written by Eugene L. Allgower and published by American Mathematical Soc.. This book was released on 1993 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry plays an important role in theoretical physics, applied analysis, classical differential equations, and bifurcation theory. Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis, there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work. This book contains the proceedings of an AMS-SIAM Summer Seminar in Applied Mathematics, held in 1992 at Colorado State University. The seminar, which drew about 100 scientists from around the world, was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods. The papers in this volume have been refereed and will not be published elsewhere.
Download or read book Twelve Papers on Algebra and Real Functions written by S. N. Cernikov and published by American Mathematical Soc.. This book was released on 1961-12-31 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt:
