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arXiv · 2105.10800

On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series

Yury A. Neretin
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Abstract

We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal covering of the group $SL(2\,{\mathbb R}$. Our main purpose is a search of natural bases in generalized eigenspaces and variants of the inversion formula.

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BibTeXRIS

Yury A. Neretin. 2021-05-22. On a ${\mathbb C}^2$-valued integral index transform and bilateral hypergeometric series. https://doi.org/10.1080/10652469.2022.2050721

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