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Author : Y. Okuyama
Publisher : Springer
Page : 125 pages
File Size : 45,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540389026
Author : Anonim
Publisher : Unknown
Page : 117 pages
File Size : 50,8 Mb
Release : 1984
Category : Electronic
ISBN : OCLC:499230507
Author : Boris Osilenker
Publisher : World Scientific
Page : 296 pages
File Size : 52,8 Mb
Release : 1999-04-01
Category : Mathematics
ISBN : 9789814495226
This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L2μ; summability almost everywhere by the Cesaro means and the Poisson–Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory. Contents:Orthogonal Polynomials and Their PropertiesConvergence and Summability of Fourier Series in L2μFourier Orthogonal Series in Lrμ (1
Author : Ferenc Weisz
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 50,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401731836
The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].
Author : Johann Boos
Publisher : Clarendon Press
Page : 616 pages
File Size : 43,9 Mb
Release : 2000
Category : Mathematics
ISBN : 019850165X
Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.
Author : Sandeep Singh,Mehmet Ali Sarigöl,Alka Munjal
Publisher : Springer Nature
Page : 242 pages
File Size : 47,7 Mb
Release : 2023-01-16
Category : Mathematics
ISBN : 9783031190827
The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics. This broad coverage will help generate new ideas to solve various challenges that face researchers in pure mathematics. Specific topics covered include maximal rotational hypersurfaces, k-Horadam sequences, quantum dynamical semigroups, and more. Additionally, several applications of algebraic number theory and analysis are presented. Algebra, Analysis, and Associated Topics will appeal to researchers, graduate students, and engineers interested in learning more about the impact pure mathematics has on various fields.
Author : József Attila Tudományegyetem
Publisher : Unknown
Page : 838 pages
File Size : 45,6 Mb
Release : 1995
Category : Mathematics
ISBN : UCAL:B4477829
Author : Anonim
Publisher : Unknown
Page : 418 pages
File Size : 52,9 Mb
Release : 1993
Category : Mathematics
ISBN : CORNELL:31924096116797
Author : Charles Sparks Rees,S. M. Shah,Caslav V. Stanojevic
Publisher : CRC Press
Page : 432 pages
File Size : 48,8 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0824769031
Trignometric sums; Integrability of trigonometric sums; Convergence and cesaro summability of fourier series; Convergence and summability of trigonetric series; Multiple fourier series; Fourier transform and applications; Orthogonal systems; Bessel functions.
Author : Robert Ellis Powell,S. M. Shah
Publisher : Unknown
Page : 196 pages
File Size : 45,7 Mb
Release : 1972
Category : Mathematics
ISBN : UCAL:B4406731
Author : Carlos A. Berenstein
Publisher : Springer
Page : 369 pages
File Size : 51,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540478935
Author : Steven G. Krantz
Publisher : Springer
Page : 207 pages
File Size : 51,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540477525
This conference gathered together a small group of people with similar interests in the geometric function theory of several complex variables. While the speeches were of a specialized nature, the papers in the proceedings are largely of a survey and speculative nature. The volume is intended to serve both students and researchers as an invitation to active new areas of research. The level of the writing has been intentionally set in such a way that the papers will be accessible to a broad audience.
Author : Sebastian S. Koh
Publisher : Springer
Page : 111 pages
File Size : 46,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479086
This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. This collection of papers centers on constructive aspects of invariant theory and opens with an introduction to the subject by F. Grosshans. Its purpose is to make the current research more accesssible to mathematicians in related fields.
Author : Marie-Paule Malliavin
Publisher : Springer
Page : 427 pages
File Size : 40,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540396284
Author : Stephen D. Comer
Publisher : Springer
Page : 290 pages
File Size : 45,6 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540396383