Frontiers in Interpolation and Approximation

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CRC Press, Jul 20, 2006 - Mathematics - 431 pages
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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.
 

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Contents

MarkovType Inequalities for Homogeneous Polynomials on Nonsymmetric StarLike Domains
1
Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions
17
The Norm of an Interpolation Operator on HD
33
The Dutch Connection
45
Freeness of Spline Modules from a Divided to a Subdivided Domain
59
Measures of Smoothness on the Sphere
75
Quadrature Formulae of Maximal Trigonometric Degree of Precision
93
Inequalities for Exponential Sums via Interpolation and TuránType Reverse Markov Inequalities
119
Lagrange Interpolation at Lacunary Roots of Unity
249
A Fast Algorithm for Spherical Basis Approximation
259
Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros
287
Fourier Sums and Lagrange Interpolation on 0+ and +
307
On Bounded Interpolatory and QuasiInterpolatory Polynomial Operators
345
Hausdorff Strong Uniqueness in Simultaneous Approximation
365
Zeros of Polynomials Given as an Orthogonal Expansion
381
Uniqueness of Tchebycheff Spaces and Their Ideal Relatives
407

Asymptotic Optimality in TimeFrequency Localization of Scaling Functions and Wavelets
145
Interpolation by Polynomials and Transcendental Entire Functions
173
Hyperinterpolation on the Sphere
213

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