Frontiers in Interpolation and Approximation  book cover
1st Edition

Frontiers in Interpolation and Approximation

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ISBN 9781584886365
Published July 20, 2006 by Chapman and Hall/CRC
476 Pages 11 B/W Illustrations

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Book Description

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

Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains

Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions

The Norm of an Interpolation Operator on H8(D)

Sharma and Interpolation

Freeness of Spline Modules from a Divided to a Subdivided Domain

Measures of Smoothness on the Sphere

Quadrature Formulae of Maximal Trigonometric Degree of Precision

Inequalities for Exponential Sums via Interpolation and TurĂ¡n-Type Reverse Markov Inequalities

Asymptotic Optimality in Time-Frequency Localization of Scaling
Functions and Wavelets

Interpolation by Polynomials and Transcendental Entire Functions
Hyperinterpolation on the Sphere

Lagrange Interpolation at Lacunary Roots of Unity

A Fast Algorithm for Spherical Basis Approximation

Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights having Zeros

Fourier Sums and Lagrange Interpolation on (0,+8) and (-8,+8)

On Bounded Interpolatory and Quasi-Interpolatory Polynomial Operators

Hausdorff Strong Uniqueness in Simultaneous Approximation

Zeros of Polynomials Given as an Orthogonal Expansion

Uniqueness of Tchebycheff Spaces and their Ideal Relatives

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