eBook Approximation Theory and Harmonic Analysis on Spheres and Balls, 1st Edition

  • Published By:
  • ISBN-10: 1461466601
  • ISBN-13: 9781461466604
  • DDC: 511.4
  • Grade Level Range: College Freshman - College Senior
  • 440 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013
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This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area.  While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes.  The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography.This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Spherical Harmonics.
2: Convolution Operator and Spherical Harmonic Expansion.
3: Littlewood-Paley Theory and the Multiplier Theorem.
4: Approximation on the Sphere.
5: Weighted Polynomial Inequalities.
6: Cubature Formulas on Spheres.
7: Harmonic Analysis Associated with Reflection Groups.
8: Boundedness of Projection Operators and Cesàro Means.
9: Projection Operators and Cesàro Means in Lp Spaces.
10: Weighted Best Approximation by Polynomials.
11: Harmonic Analysis on the Unit Ball.
12: Polynomial Approximation on the Unit Ball.
13: Harmonic Analysis on the Simplex.
14: Applications.
Distance, Difference and Integral Formulas.
Jacobi and Related Orthogonal Polynomials.
Symbol Index.