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Overconvergence in Complex Approximation [electronic resource] / by Sorin G. Gal.

By: Gal, Sorin G [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: New York, NY : Springer New York : Imprint: Springer, 2013Description: XIV, 194 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461470984.Subject(s): Mathematics | Functions of complex variables | Differential equations, partial | Mathematics | Approximations and Expansions | Functions of a Complex Variable | Several Complex Variables and Analytic SpacesDDC classification: 511.4 Online resources: Click here to access online
Contents:
Overconvergence in C of Some Bernstein-Type Operators -- Overconvergence and Convergence in C of Some Integral Convolutions -- Overconvergence in C of the Orthogonal Expansions .
In: Springer eBooksSummary: 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.
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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.

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