On matrix valued square integrable positive definite functions
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
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