Back to Search
Start Over
Quaternion-valued positive definite functions on locally compact Abelian groups and nuclear spaces.
- Source :
-
Applied Mathematics & Computation . Aug2016, Vol. 286, p115-125. 11p. - Publication Year :
- 2016
-
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 R N = { ( x 1 , x 2 , … ) : x d ∈ 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 286
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 115367760
- Full Text :
- https://doi.org/10.1016/j.amc.2016.03.034