Overview
Presents quantitative overconvergence results in complex approximation
Generalizes and extends the results for certain cases of the complex q-Bernstein operators
Includes a notes and open problems section at the end of each chapter, promoting future research
Includes supplementary material: sn.pub/extras
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Table of contents (3 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Overconvergence in Complex Approximation
Authors: Sorin G. Gal
DOI: https://doi.org/10.1007/978-1-4614-7098-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-7097-7Published: 27 April 2013
Softcover ISBN: 978-1-4899-9791-3Published: 20 May 2015
eBook ISBN: 978-1-4614-7098-4Published: 08 July 2014
Edition Number: 1
Number of Pages: XIV, 194
Topics: Approximations and Expansions, Functions of a Complex Variable, Several Complex Variables and Analytic Spaces