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

Daniel Alpay, Fabrizio Colombo, David P. Kimsey and Irene Sabadini

Applied Mathematics and Computation, 2016, vol. 286, issue C, 115-125

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,…):xd∈R}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.

Keywords: Bochner's theorem; Bochner-Minlos theorem; quaternionic analysis; nuclear spaces (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:286:y:2016:i:c:p:115-125

DOI: 10.1016/j.amc.2016.03.034

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