On functions on a sphere with zero integrals over circumferences with fixed radius
type: Item
instance of: scholarly article
title: On functions on a sphere with zero integrals over circumferences with fixed radius
zbMATH Open document ID: 1345.43006
author: Irina M. Savost'yanova
author: Valeriĭ V. Volchkov
author: Vit. V. Volchkov
published in: Journal of Mathematical Sciences (New York)
publication date: 2016-01-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 6532888
zbMATH Keywords: spherical means
zbMATH Keywords: Legendre function
zbMATH Keywords: theorems of two radii
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
full work available at URL: s10958-015-2625-9
OpenAlex ID: W2237692693
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DOI: 10.1007/S10958-015-2625-9
description: scientific article; zbMATH DE number 6532888