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Approximation Theory
In Memory of A.K. Varma




ISBN 9780824701857
Published May 12, 1998 by CRC Press
552 Pages

 
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Book Description

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Table of Contents

Error bounds for the derivatives of Lidstone interpolation and applications; higher order univariate wavelet typed approximation; modified weighted (0.2) interpolation; new approach to Markov inequality in Lp norms; a question of reliability theory; notes on miscellaneous approximation problems; Muntz's theorem on compact subsets of positive measure; frames and Schauder bases; interpolation on spheres; nonparametric density estimation by polynomials and by splines; Birkhoff type interpolation on perturbed roots of unity; approximation by entire functions with only real zeros; nonlinear means in geometric modelling; nonlinear stationary subdivision; convex univalent functions and omitted values; total positivity and total variation; inequalities for maximum modulus of rational functions with prescribed poles; recent progress on multivariate splines; hermite interpolation on Chebyshev nodes and Walsh equiconvergence; continuous functions which change sign without properly crossing the x-axis; some remarks on weighted interpolation; a note on Chebyshev's inequality; smooth Maclaurin series coefficients in Pade and rational approximation; on Marcinkiewicz-Zygmund-type inequalities; extremal problems for restricted polynomial classes in Lp norm.

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Reviews

"This volume consists of invited papers paying tribute to the late Arun Kiumar Varma. Varma's main interest in mathematics was centered around lacunary interpolation and around polynomial inequalities. . .. This volume is an appropriate memorial to a devoted mathematician whose untimely death prevented completing many projects that were under way or were unplanned. With this volume his memory lives on through outstanding contributions by students, friends and followers. "
---Acta Sci. Math.