Titlebook: Approximation Theory and Harmonic Analysis on Spheres and Balls; Feng Dai,Yuan Xu Book 2013 Springer Science+Business Media New York 2013

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Harmonic Analysis on the Unit Ball, however, that analysis on the unit ball is closely related to analysis on the unit sphere. Indeed, a large portion of harmonic analysis on the unit ball can be deduced from its counterparts on the sphere.

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Harpoon

Harmonic Analysis Associated with Reflection Groups,ighted approximation and harmonic analysis on the sphere, which turn out to be indispensable for the corresponding theory, even for unweighted approximation and harmonic analysis, on the unit ball and on the simplex, as will be seen in later chapters.

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1439-7382 ful research material for both experts and advanced graduate.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 mate

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https://doi.org/10.1007/978-3-662-32547-6the Poisson integrals for the Fourier expansion in spherical harmonics, discussed in the second section, are convolution operators, which are also multiplier operators. The convolution and translation operators are used to define and study the Hardy–Littlewood maximal function on the sphere in the third section.

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Lasting

Zeitschrift für die gesamte Anatomiech results for .-harmonic expansions with respect to the product ., which cover results for ordinary spherical harmonic expansions. The proof of such results depends on the boundedness of proj ection operators, which will be established in the first section, assuming a critical estimate.

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