Symmetry problems in harmonic analysis

• Alexander G. Ramm ^[1]
  1. [1] Kansas State University

     Kansas State University

     City of Manhattan, Estados Unidos

     
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 78, Nº. 1, 2021, págs. 155-158
• Idioma: inglés
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• Resumen

  • 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.