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The distributional products on spheres and Pizetti’s formula

✍ Scribed by C.K. Li; M.A. Aguirre

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
229 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

The distribution δ (k) (ra) concentrated on the sphere O a with ra = 0 is defined as

Taking the Fourier transform of the distribution and the integral representation of the Bessel function, we obtain asymptotic expansions of δ (k) (ra) for k = 0, 1, 2, . . . in terms of △ j δ(x 1 , . . . , x n ), in order to show the well-known Pizetti formula by a new method. Furthermore, we derive an asymptotic product of φ(x 1 , . . . ,

, where φ is an infinitely differentiable function, based on the formula of △ m (φψ), and hence we are able to characterize the distributions focused on spheres, which can be written as the sums of multiplet layers in the Gel'fand sense.

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