Overconvergence in Complex Approximation

Sorin G. Gal

ISBN 10: 1489997911 / ISBN 13: 9781489997913

Published by Springer New York Mai 2015, 2015

About this Item

This item is printed on demand - it takes 3-4 days longer - 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 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. 208 pp. Englisch.

Seller Inventory # 9781489997913

Bibliographic Details

• Title: Overconvergence in Complex Approximation
• Publisher: Springer New York Mai 2015
• Publication Date: 2015
• Language: English
• ISBN 10: 1489997911
• ISBN 13: 9781489997913
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 12D millimeters 235 millimeters width by 155 millimeters height by 12 millimeters depth
• Weight: 324 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.