Approximation Theory and Harmonic Analysis on Spheres and Balls

Feng Dai, Yuan Xu (Autoren)

Buch | Softcover

440 Seiten

2015
Springer-Verlag New York Inc.
978-1-4939-0131-9 (ISBN)

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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.

Feng Dai is currently a professor of mathematics at the University of Alberta, and Yuan Xu is currently a professor of mathematics at the University of Oregon.

1 Spherical Harmonics.- 2 Convolution and Spherical Harmonic Expansion.- 3 Littlewood-Paley Theory and Multiplier Theorem.- 4 Approximation on the Sphere.- 5 Weighted Polynomial Inequalities.- 6 Cubature Formulas on Spheres.- 7 Harmonic Analysis Associated to Reflection Groups.- 8 Boundedness of Projection Operator and Cesàro Means.- 9 Projection Operators and Cesàro Means in L^p 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.- A Distance, Difference and Integral Formulas.- B Jacobi and Related Orthogonal Polynomials.- References.- Index.- Symbol Index.

Erscheint lt. Verlag	22.5.2015
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XVIII, 440 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4939-0131-1 / 1493901311
ISBN-13	978-1-4939-0131-9 / 9781493901319
Zustand	Neuware