Polynomial Expansions Of Analytic Functions

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Polynomial expansions of analytic functions

Author : Ralph P. Boas
Publisher : Springer Science & Business Media
ISBN 13 : 3662251701
Total Pages : 85 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Polynomial expansions of analytic functions by : Ralph P. Boas

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.

Polynomial Expansions of Analytic Functions

Author : Ralph P.Jr. Boas
Publisher : Springer Science & Business Media
ISBN 13 : 3642878873
Total Pages : 85 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Polynomial Expansions of Analytic Functions by : Ralph P.Jr. Boas

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.

Polynomial expansions of analytic functions

Author : Ralph P. Boas (Jr.)
Publisher :
ISBN 13 :
Total Pages : 77 pages
Book Rating : 4.:/5 (872 download)

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Book Synopsis Polynomial expansions of analytic functions by : Ralph P. Boas (Jr.)

Download or read book Polynomial expansions of analytic functions written by Ralph P. Boas (Jr.) and published by . This book was released on 1958 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Note on Least-square Approximation to an Analytic Function by Polynomials, as Measured by a Surface Integral

Author : Joseph Leonard Walsh
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Note on Least-square Approximation to an Analytic Function by Polynomials, as Measured by a Surface Integral by : Joseph Leonard Walsh

Download or read book Note on Least-square Approximation to an Analytic Function by Polynomials, as Measured by a Surface Integral written by Joseph Leonard Walsh and published by . This book was released on 1958 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Theory of Polynomials

Author : Qazi Ibadur Rahman
Publisher : Oxford University Press
ISBN 13 : 9780198534938
Total Pages : 760 pages
Book Rating : 4.5/5 (349 download)

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Book Synopsis Analytic Theory of Polynomials by : Qazi Ibadur Rahman

Download or read book Analytic Theory of Polynomials written by Qazi Ibadur Rahman and published by Oxford University Press. This book was released on 2002 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications

Degree of Polynomial Approximation to an Analytic Function as Measured by a Surface Integral

Author : Joseph Leonard Walsh
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Degree of Polynomial Approximation to an Analytic Function as Measured by a Surface Integral by : Joseph Leonard Walsh

Download or read book Degree of Polynomial Approximation to an Analytic Function as Measured by a Surface Integral written by Joseph Leonard Walsh and published by . This book was released on 1961 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results are derived relating continuity properties of f(z) on the boundary C of a region D to D f(z) - pn(z) pdS, p> 1, as a measure ofAPPROXIMATION. (Author).

A Unified Approach to Uniqueness, Expansion and Approximation Problems

Author : Chiu-Cheng Chang
Publisher : World Scientific
ISBN 13 : 9789810218058
Total Pages : 132 pages
Book Rating : 4.2/5 (18 download)

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Book Synopsis A Unified Approach to Uniqueness, Expansion and Approximation Problems by : Chiu-Cheng Chang

Download or read book A Unified Approach to Uniqueness, Expansion and Approximation Problems written by Chiu-Cheng Chang and published by World Scientific. This book was released on 1994 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the concept of P¢lya property for holomorphic functions of two and several variables. The functions which have the P¢lya property are used to study the uniqueness problem for entire functions. This gives interesting results for a general class of generating functions. The functions with P¢lya property are also used as generating kernels in formal generating relations to study the expansion problem for entire functions. A necessary and sufficient condition is obtained for an entire function to have a unique expansion in a series of various known polynomials generated from the formal generating relations.In this book, it is shown that the uniqueness problem for entire functions of exponential type is equivalent to the approximation problem for analytic functions. This result, in combination with other results, produces many interesting theorems on the approximation of analytic functions. Since functions with P¢lya property have very useful applications, the study of a class of linear operators which preserve the P¢lya property is embarked upon and two sufficient conditions for an operator to be P¢lya-property-preserving are given.

Series of Faber Polynomials

Author : P.K. Suetin
Publisher : CRC Press
ISBN 13 : 9789056990589
Total Pages : 328 pages
Book Rating : 4.9/5 (95 download)

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Book Synopsis Series of Faber Polynomials by : P.K. Suetin

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.

Analytic Function Theory

Author : Einar Hille
Publisher : American Mathematical Soc.
ISBN 13 : 9780821829141
Total Pages : 510 pages
Book Rating : 4.8/5 (291 download)

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Book Synopsis Analytic Function Theory by : Einar Hille

Download or read book Analytic Function Theory written by Einar Hille and published by American Mathematical Soc.. This book was released on 2002 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.

Polyanalytic Functions

Author : Mark Benevich Balk
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Polyanalytic Functions by : Mark Benevich Balk

Download or read book Polyanalytic Functions written by Mark Benevich Balk and published by Wiley-VCH. This book was released on 1991-11-13 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Functions of Several Complex Variables

Author : Robert Clifford Gunning
Publisher : American Mathematical Soc.
ISBN 13 : 0821821652
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analytic Functions of Several Complex Variables by : Robert Clifford Gunning

Download or read book Analytic Functions of Several Complex Variables written by Robert Clifford Gunning and published by American Mathematical Soc.. This book was released on 2009 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.

Graduate Mathematical Physics

Author : James J. Kelly
Publisher : John Wiley & Sons
ISBN 13 : 3527618902
Total Pages : 482 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Graduate Mathematical Physics by : James J. Kelly

Download or read book Graduate Mathematical Physics written by James J. Kelly and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date textbook on mathematical methods of physics is designed for a one-semester graduate or two-semester advanced undergraduate course. The formal methods are supplemented by applications that use MATHEMATICA to perform both symbolic and numerical calculations. The book is written by a physicist lecturer who knows the difficulties involved in applying mathematics to real problems. As many as 40 exercises are included at the end of each chapter. A student CD includes a basic introduction to MATHEMATICA, notebook files for each chapter, and solutions to selected exercises. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Entire Functions

Author :
Publisher : Academic Press
ISBN 13 : 9780080873138
Total Pages : 275 pages
Book Rating : 4.8/5 (731 download)

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Book Synopsis Entire Functions by :

Download or read book Entire Functions written by and published by Academic Press. This book was released on 2011-08-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entire Functions

Mathematical Analysis in Interdisciplinary Research

Author : Ioannis N. Parasidis
Publisher : Springer Nature
ISBN 13 : 3030847217
Total Pages : 1050 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematical Analysis in Interdisciplinary Research by : Ioannis N. Parasidis

Download or read book Mathematical Analysis in Interdisciplinary Research written by Ioannis N. Parasidis and published by Springer Nature. This book was released on 2022-03-10 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

Introduction to the Theory of Entire Functions

Author :
Publisher : Academic Press
ISBN 13 : 9780080873718
Total Pages : 220 pages
Book Rating : 4.8/5 (737 download)

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Book Synopsis Introduction to the Theory of Entire Functions by :

Download or read book Introduction to the Theory of Entire Functions written by and published by Academic Press. This book was released on 1974-02-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Entire Functions

Polynomials

Author : Cheon Seoung Ryoo
Publisher : BoD – Books on Demand
ISBN 13 : 183880269X
Total Pages : 174 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Polynomials by : Cheon Seoung Ryoo

Download or read book Polynomials written by Cheon Seoung Ryoo and published by BoD – Books on Demand. This book was released on 2019-05-02 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Walsh Equiconvergence of Complex Interpolating Polynomials

Author : Amnon Jakimovski
Publisher : Springer Science & Business Media
ISBN 13 : 1402041756
Total Pages : 303 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Walsh Equiconvergence of Complex Interpolating Polynomials by : Amnon Jakimovski

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.