On matrix valued square integrable positive definite functions

Authors

Hongyu He, Louisiana State University

Document Type

Article

Publication Date

7-12-2015

Abstract

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two theorems of Godement on L² positive definite functions. We show that a matrix-valued continuous L² positive definite function can always be written as the convolution of a matrix-valued L² positive definite function with itself. We also prove that, given two L² matrix valued positive definite functions (Formula presented.). In addition this integral equals zero if and only if Φ∗Ψ=0. Our proofs are operator-theoretic and independent of the group.

Publication Source (Journal or Book title)

Monatshefte fur Mathematik

First Page

437

Last Page

449

Recommended Citation

He, H. (2015). On matrix valued square integrable positive definite functions. Monatshefte fur Mathematik, 177 (3), 437-449. https://doi.org/10.1007/s00605-015-0732-9