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- W4289744706 abstract "In this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in cite{Bia1} from the restriction of a particular positive definite function on the complex unimodular group $Sl(2,mathbb{C})$ to two commutative subalgebras of its universal $C^{star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well, occurring between the heat kernel on the Heisenberg group and the semi-group corresponding to the intersection of the principal and the complementary series. To this end, we appeal to the metaplectic representation $Mp(4,mathbb{R})$ and to the Landau operator in the complex plane." @default.
- W4289744706 created "2022-08-04" @default.
- W4289744706 creator A5066962638 @default.
- W4289744706 date "2018-07-24" @default.
- W4289744706 modified "2023-09-25" @default.
- W4289744706 title "Markov semi-groups associated with the complex unimodular group $Sl(2,mathbb{C})$" @default.
- W4289744706 doi "https://doi.org/10.48550/arxiv.1807.09238" @default.
- W4289744706 hasPublicationYear "2018" @default.
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