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

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.

16p

References in corpus (2)

• A pair of commuting hypergeometric operators on the complex plane and bispectrality
• An analog of the Dougall formula and of the de Branges--Wilson integral