Overconvergence in Complex Approximation

  • Sorin G. Gal

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Back Matter
    Pages 185-194

About this book

Introduction

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/q^n 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.

Keywords

approximation by complex Bernstein-type operators approximation by complex potential of Euler-type overconvergence of complex orthogonal polynomials overconvergence phenomenon quantitative overconvergence

Authors and affiliations

  • Sorin G. Gal
    • 1
  1. 1., Dept of Mathematics and Computer ScienceUniversity of OradeaOradeaRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7098-4
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7097-7
  • Online ISBN 978-1-4614-7098-4
  • About this book