Frontiers in Interpolation And Approximation

by Govil; N. K.

• ISBN13: 9781584886365
• ISBN10: 1584886366
• eBook ISBN(s): 9781040207888
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-07-20
• Publisher: Chapman & Hall/
• More Book Details

Summary

Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis.Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions.Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.

Table of Contents

Foreword	ix
R. S. Varga
Preface	xi
Editors	xv
Contributors	xvii
Ambikeshwar Sharma	xxiii
A. Jakimovski
J. Szabados
Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains	1	(16)
Yuliya Babenko
Andras Kroo
Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions	17	(16)
A. Brudnyi
Yu. Brudnyi
The Norm of an Interpolation Operator on H∞(D)	33	(12)
A. S. Cavaretta
N. Fontes-Merz
Sharma and Interpolation, 1993--2003: The Dutch Connection	45	(14)
M. G. de Bruin
Freeness of Spline Modules from a Divided to a Subdivided Domain	59	(16)
Satya Deo
J. K. Maitra
Measures of Smoothness on the Sphere	75	(18)
Z. Ditzian
Quadrature Formulae of Maximal Trigonometric Degree of Precision	93	(26)
Dimiter Dryanov
Inequalities for Exponential Sums via Interpolation and Turan-Type Reverse Markov Inequalities	119	(26)
T. Erdelyi
Asymptotic Optimality in Time-Frequency Localization of Scaling Functions and Wavelets	145	(28)
T. N. T. Goodman
S. L. Lee
Interpolation by Polynomials and Transcendental Entire Functions	173	(40)
N. K. Govil
M. A. Qazi
Q. I. Rahman
Hyperinterpolation on the Sphere	213	(36)
Kerstin Hesse
Ian H. Sloan
Lagrange Interpolation at Lacunary Roots of Unity	249	(10)
A. Jakimovski
A Fast Algorithm for Spherical Basis Approximation	259	(28)
J. Keiner
J. Prestin
Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros	287	(20)
G. Mastroianni
J. Szabados
Fourier Sums and Lagrange Interpolation on (0, + ∞) and (-∞, + ∞)	307	(38)
G. Mastroianni
P. Vertesi
On Bounded Interpolatory and Quasi--Interpolatory Polynomial Operators	345	(20)
H. N. Mhaskar
Hausdorff Strong Uniqueness in Simultaneous Approximation. Part II	365	(16)
Devidas Pai
Indira K
Zeros of Polynomials Given as an Orthogonal Expansion	381	(26)
Gerhard Schmeisser
Uniqueness of Tchebycheff Spaces and Their Ideal Relatives	407	(20)
Boris Shekhtman
Index	427