In this paper we study quaternion-valued positive definite functions on locally compact Abelian groups, real countably Hilbertian nuclear spaces and on the space RN=(x1,x2,...):xdϵR endowed with the Tychonoff topology. In particular, we prove a quaternionic version of the Bochner-Minlos theorem. A tool for proving this result is a classical matricial analogue of the Bochner-Minlos theorem, which we believe is new. We will see that in all these various settings the integral representation is with respect to a quaternion-valued measure which has certain symmetry properties.

Quaternion-valued positive definite functions on locally compact Abelian groups and nuclear spaces

COLOMBO, FABRIZIO;SABADINI, IRENE MARIA
2016-01-01

Abstract

In this paper we study quaternion-valued positive definite functions on locally compact Abelian groups, real countably Hilbertian nuclear spaces and on the space RN=(x1,x2,...):xdϵR endowed with the Tychonoff topology. In particular, we prove a quaternionic version of the Bochner-Minlos theorem. A tool for proving this result is a classical matricial analogue of the Bochner-Minlos theorem, which we believe is new. We will see that in all these various settings the integral representation is with respect to a quaternion-valued measure which has certain symmetry properties.
2016
Bochner's theorem; Bochner-Minlos theorem; nuclear spaces; quaternionic analysis; Computational Mathematics; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1007254
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