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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2005 Volume 327, Pages 207–225 (Mi znsl331)

Riesz potentials associated with the composite power function on the space of rectangular matrices

S. P. Khekalo

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: On the space of real rectangular matrices, Riesz potentials depending on a multidimensional complex parameter are studied. These potentials are in relationship with the composite power function of a matrix argument. For the potentials indicated, analogs of classical equalities are established. In particular, the semigroup property for the Riesz potentials with multidimensional complex parameter is proved under less restrictive limitations on the parameters of a rectangular matrix than the corresponding semigroup property for the Riesz potentials of one complex parameter.

UDC: 517.944

Received: 15.09.2005


 English version:
Journal of Mathematical Sciences (New York), 2006, 139:2, 6479–6490

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© Steklov Math. Inst. of RAS, 2025