On Matrix-Valued Square Integrable Positive Definite Functions

Details On Matrix-Valued Square Integrable Positive Definite Functions On Matrix-Valued Square Integrable Positive Definite Functions

2009-05-01

arxiv.org/abs/0905.0169v2

Mathematics

Operator Algebras

10 pages

Scientific paper

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions. We show that a matrix-valued continuous $L^2$ positive definite function can always be written as a convolution of a $L^2$ positive definite function with itself. We also prove that, given two $L^2$ matrix valued positive definite functions $\Phi$ and $\Psi$, $\int_G Trace(\Phi(g) \bar{\Psi(g)}^t) d g \geq 0$. In addition this integral equals zero if and only if $\Phi * \Psi=0$. Our proofs are operator-theoretic and independent of the group.

Affiliated with

Also associated with

No associations

Rating

On Matrix-Valued Square Integrable Positive Definite Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Matrix-Valued Square Integrable Positive Definite Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Matrix-Valued Square Integrable Positive Definite Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-100819