
Topics in Complex Approximation
£ 60.00
G. Anastassiou
University of Memphis, USA
This monograph studies quantitatively the order of simultaneous approximation and Voronovskaja type asymptotic results for complex Bernstein-Schurer, Kantorovich-Schurer and Bernstein-Durrmeyer polynomials related to analytic functions on compact disks. In this way the overconvergence phenomenon for Bernstein-Schurer and Bernstein-Durrmeyer polynomials is revealed. We continue with explicit quantitative estimates for the overconvergence in the complex plane of the partial sums of the Fourier-type expansions on [-1, 1] with respect to Chebyshev and Legendre orthogonal polynomials.
2013 Pbk ISBN 978-1-908106-21-6 250pp
Description
G. Anastassiou
University of Memphis, USA
This monograph studies quantitatively the order of simultaneous approximation and Voronovskaja type asymptotic results for complex Bernstein-Schurer, Kantorovich-Schurer and Bernstein-Durrmeyer polynomials related to analytic functions on compact disks. In this way the overconvergence phenomenon for Bernstein-Schurer and Bernstein-Durrmeyer polynomials is revealed. We continue with explicit quantitative estimates for the overconvergence in the complex plane of the partial sums of the Fourier-type expansions on [-1, 1] with respect to Chebyshev and Legendre orthogonal polynomials. Furthermore we obtain quantitative estimates in the overconvergence phenomenon for the classical and generalized singular integrals of Gauss-Weierstrass, Poisson-Cauchy and Picard on a strip. This monograph is intended for researchers, graduate students working in many areas of pure and applied mathematics.
2013 Pbk ISBN 978-1-908106-21-6 250pp
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