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＜E-Book＞
Overconvergence in Complex Approximation / by Sorin G. Gal

Edition	1st ed. 2013.
Publisher	New York, NY : Springer New York : Imprint: Springer
Year	2013
Language	English
Size	XIV, 194 p : online resource
Authors	*Gal, Sorin G author SpringerLink (Online service)
Subjects	LCSH:Approximation theory LCSH:Functions of complex variables FREE:Approximations and Expansions FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces
Notes	Overconvergence in C of Some Bernstein-Type Operators -- Overconvergence and Convergence in C of Some Integral Convolutions -- Overconvergence in C of the Orthogonal Expansions 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 HTTP:URL=https://doi.org/10.1007/978-1-4614-7098-4

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