On Matrix Valued Square Integrable Positive Definite Functions
نویسنده
چکیده
In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on L positive definite functions to matrix valued L positive definite functions. We show that a matrix-valued continuous L positive definite function can always be written as a convolution of a L positive definite function with itself. We also prove that, given two L matrix valued positive definite functions Φ and Ψ, R G Trace(Φ(g)Ψ(g) t )dg ≥ 0. In addition this integral equals zero if and only if Φ ∗ Ψ = 0. Our proofs are operator-theoretic and independent of the group.
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