30 citations · 178 across the 55 of their papers we have counts for
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Spherical harmonics, operators of multiplication by coordinates, and infinitesimal conformal transformations
Yury A. Neretin
Consider the space of -functions on the two-dimensional sphere and its decomposition into a direct sum of minimal rotation-invariant spaces. We…
On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
Yury A. Neretin
The Selberg integral has a twin (`the Dotsenko--Fateev integral') of the following form. We replace real variables in the integrand $\prod |x_k|^{σ-1}\,|1-x_k|^{τ-1} \prod|x_…
On a -valued integral index transform and bilateral hypergeometric series
Yury A. Neretin
We discuss the spectral decomposition of the hypergeometric differential operators on the line . Such operators arise in the problem of decomposition of tensor…
Barnes-Ismagilov integrals and hypergeometric functions of the complex field
Yury A. Neretin
We examine a family of integrals of Mellin-Barnes type over the space , such functio…
An analog of the Dougall formula and of the de Branges--Wilson integral
Yury A. Neretin
We derive a beta-integral over , which is a counterpart of the Dougall -formula and of the de Branges--Wilson integral, our integral includes $…
Matrix beta-integrals: an overview
Yury A. Neretin
First examples of matrix beta-integrals were discovered on 1930-50s by Siegel and Hua, in 60s Gindikin obtained multi-parametric series of such integrals. We discuss beta-integrals…
Hua type beta-integrals and projective systems of measures on flag spaces
Yury A. Neretin
We construct a family of measures on flag spaces (or, equivalently, on the spaces of upper-triangular matrices) compatible with respect to natural projections. We obtain an $n(n-1)…
Index hypergeometric integral transform
Yury A. Neretin
This is a brief overview of the index hypergeometric transform (other terms for this integral operator are: Olevskii transform, Jacobi transform, generalized Mehler--Fock transform…