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.
Author(s): N. K. Govil, H. N. Mhaskar, Ram N. Mohapatra, Zuhair Nashed, J. Szabados
Series: Monographs and Textbooks in Pure and Applied Mathematics
Edition: 1
Publisher: Crc Pr Inc
Year: 2006
Language: English
Pages: 476
Cover......Page 1
Title......Page 6
Copyright......Page 7
Contents......Page 8
Foreword......Page 10
Preface......Page 12
EDITORS......Page 16
Contributors......Page 18
Ambikeshwar Sharma......Page 24
Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains......Page 46
Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions......Page 62
The Norm of an Interpolation Operator on H∞(D)......Page 78
Sharma and Interpolation, 1993–2003: The Dutch Connection......Page 90
Freeness of Spline Modules from a Divided to a Subdivided Domain......Page 104
Measures of Smoothness on the Sphere......Page 120
Quadrature Formulae of Maximal Trigonometric Degree of Precision......Page 138
Inequalities for Exponential Sums via Interpolation and Turán-Type Reverse Markov Inequalities......Page 164
Asymptotic Optimality in Time-Frequency Localization of Scaling Functions and Wavelets......Page 190
Interpolation by Polynomials and Transcendental Entire Functions......Page 218
Hyperinterpolation on the Sphere......Page 258
Lagrange Interpolation at Lacunary Roots of Unity......Page 294
A Fast Algorithm for Spherical Basis Approximation......Page 304
Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros......Page 332
Fourier Sums and Lagrange Interpolation on (0,+∞) and (-∞,+∞)......Page 352
On Bounded Interpolatory and Quasi-Interpolatory Polynomial Operators......Page 390
Hausdorff Strong Uniqueness in Simultaneous Approximation......Page 410
Zeros of Polynomials Given as an Orthogonal Expansion......Page 426
Uniqueness of Tchebycheff Spaces and Their Ideal Relatives......Page 452
Index......Page 472
