On functions on a sphere with zero integrals over circumferences with fixed radius
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.
scientific article; zbMATH DE number 6532888
scientific article