Riesz potentials and integral geometry in the space of rectangular matrices

• Autores: Boris Rubin
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 205, Nº 2, 2006, págs. 549-598
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.08.001
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• Resumen

  • Riesz potentials on the space of rectangular n×m matrices arise in diverse ¿higher rank¿ problems of harmonic analysis, representation theory, and integral geometry. In the rank-one case m=1 they coincide with the classical operators of Marcel Riesz. We develop new tools and obtain a number of new results for Riesz potentials of functions of matrix argument. The main topics are the Fourier transform technique, representation of Riesz potentials by convolutions with a positive measure supported by submanifolds of matrices of rank