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 Turán-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