Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4625734 | Applied Mathematics and Computation | 2016 | 11 Pages |
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,â¦):xdâR}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
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini,