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arXiv · 2402.06399

Remarks on positive definite functions on a group

Swapan Jana·Sourav Pal·Nitin Tomar
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Abstract

We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contractions. We classify all commuting unitary representations over a finite group. We show by examples that the power of a positive-definite function may not be positive definite and also the power of a unitary representation may not be a unitary representation. We also characterize all unitary representations whose powers are also unitary representations.

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Swapan Jana, Sourav Pal, Nitin Tomar. 2024-02-09. Remarks on positive definite functions on a group. https://arxiv.org/abs/2402.06399

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