Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces

Mathematics – Classical Analysis and ODEs

Scientific paper

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33 pages

Scientific paper

We discuss properties of the index hypergeometric transform (it is named also
the Jacobi transform or the Olevsky transform) interpolating analysis of
Berezin kernels on rank 1 symmetric spaces. We discuss a unitary intertwining
operator from $L^2$ on symmetric space to Berezin deformation of $L^2$. We also
find images of some differential operators under the index transform.

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