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.
CONTENTS
Foreword
Preface
Editors
Contributors
Ambikeshwar Sharma
1. Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains
2. Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions
3. The Norm of an Interpolation Operator on H1(D)
4. Sharma and Interpolation, 1993–2003: The Dutch Connection
5. Freeness of Spline Modules from a Divided to a Subdivided Domain
6. Measures of Smoothness on the Sphere
7. Quadrature Formulae of Maximal Trigonometric Degree of Precision
8. Inequalities for Exponential Sums via Interpolation and Tur´an-Type Reverse Markov Inequalities
9. Asymptotic Optimality in Time-Frequency Localization of Scaling Functions and Wavelets
10. Interpolation by Polynomials and Transcendental Entire Functions
11. Hyperinterpolation on the Sphere
12. Lagrange Interpolation at Lacunary Roots of Unity
13. A Fast Algorithm for Spherical Basis Approximation
14. Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros
15. Fourier Sums and Lagrange Interpolation on (0;+1) and (α1;+ α)
16. On Bounded Interpolatory and Quasi–Interpolatory Polynomial Operators
17. Hausdorff Strong Uniqueness in Simultaneous Approximation
18. Zeros of Polynomials Given as an Orthogonal Expansion
19. Uniqueness of Tchebycheff Spaces and Their Ideal Relatives
Index
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.
CONTENTS
Foreword
Preface
Editors
Contributors
Ambikeshwar Sharma
1. Markov-Type Inequalities for Homogeneous Polynomials on Nonsymmetric Star-Like Domains
2. Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions
3. The Norm of an Interpolation Operator on H1(D)
4. Sharma and Interpolation, 1993–2003: The Dutch Connection
5. Freeness of Spline Modules from a Divided to a Subdivided Domain
6. Measures of Smoothness on the Sphere
7. Quadrature Formulae of Maximal Trigonometric Degree of Precision
8. Inequalities for Exponential Sums via Interpolation and Tur´an-Type Reverse Markov Inequalities
9. Asymptotic Optimality in Time-Frequency Localization of Scaling Functions and Wavelets
10. Interpolation by Polynomials and Transcendental Entire Functions
11. Hyperinterpolation on the Sphere
12. Lagrange Interpolation at Lacunary Roots of Unity
13. A Fast Algorithm for Spherical Basis Approximation
14. Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros
15. Fourier Sums and Lagrange Interpolation on (0;+1) and (α1;+ α)
16. On Bounded Interpolatory and Quasi–Interpolatory Polynomial Operators
17. Hausdorff Strong Uniqueness in Simultaneous Approximation
18. Zeros of Polynomials Given as an Orthogonal Expansion
19. Uniqueness of Tchebycheff Spaces and Their Ideal Relatives
Index
Páginas : 431
Peso : 7mb.
Formato : PDF.
Edición : Primera
Año de Publicación :2006
ISBN : 978-1584886365
Editorial : Chapman and Hall/CRC
Autor N. K. Govil, H. N. Mhaskar
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