On functions on a sphere with zero integrals over circumferences with fixed radius (Q905436)
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scientific article; zbMATH DE number 6532888
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On functions on a sphere with zero integrals over circumferences with fixed radius |
scientific article; zbMATH DE number 6532888 |
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On functions on a sphere with zero integrals over circumferences with fixed radius (English)
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19 January 2016
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The paper is devoted to some generalizations of the classical ``freak theorem'' that deals with functions on \(n\)-dimensional spheres having zero integrals on some subspheres. Here the authors consider a 2-dimensional sphere possessing zero weighted means over circumferences with fixed radii. A description of such functions in the form of expansions over spherical harmonics is presented. Some analogs of theorems of \(s\) radii on \(S^2\) and new local theorems of one and two radii are obtained.
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spherical means
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Legendre function
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theorems of two radii
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