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

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

2001-04-03

arxiv.org/abs/math/0104035v1

Mathematics

Classical Analysis and ODEs

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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