Overconvergence in Complex Approximation

Sorin G. Gal

ISBN 10: 1461470978 / ISBN 13: 9781461470977

Published by Springer New York, Springer New York Apr 2013, 2013

About this Item

Neuware -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 approximation1/qnis 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 208 pp. Englisch.

Seller Inventory # 9781461470977

Bibliographic Details

• Title: Overconvergence in Complex Approximation
• Publisher: Springer New York, Springer New York Apr 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 1461470978
• ISBN 13: 9781461470977
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 16D millimeters 241 millimeters width by 160 millimeters height by 16 millimeters depth
• Weight: 483 grams

About this title

Synopsis

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.