Resumen de Symmetry problems in harmonic analysis
Symmetry problems in harmonic analysis are formulated and solved. One of these problems is equivalent to the refined Schiffer’s conjecture which was recently proved by the author. Let k=const>0 be fixed, S2 be the unit sphere in R3, D be a connected bounded domain with C2−smooth connected boundary S, j0(r) be the spherical Bessel function. The harmonic analysis symmetry problems are stated in the following theorems. Theorem A Assume that ∫Seikβ⋅sds=0 for all β∈S2. Then S is a sphere of radius a, where j0(ka)=0. Theorem B Assume that ∫Deikβ⋅xdx=0 for all β∈S2. Then D is a ball.
