Abstract
For the group G = SL(2,R), we write out explicitly differential operators intertwining irreducible finite-dimensional representations T k of G with tensor products T l ⊗ T m (we call them Poisson and Fourier transforms); we also describe an analogue of harmonic analysis and write explicit expressions for compositions of these transforms with Lie operators of the overgroup G×G. The constructions are based on a differential-difference relation for the Poisson kernel.
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Translated from Funktsional′nyi Analiz i Ego Prilozheniya, Vol. 49, No. 4, pp. 50–60, 2015 Original Russian Text Copyright © by V. F. Molchanov
This work was supported by RFBR grant no. 13-01-00952-a, by the Ministry of Education and Science of the Russian Federation under Government order no. 2014/285 (project no. 2476), and by the Regional Foundation for Assistance to Domestic Science.
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Molchanov, V.F. Poisson and fourier transforms for tensor products. Funct Anal Its Appl 49, 279–288 (2015). https://doi.org/10.1007/s10688-015-0116-x
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DOI: https://doi.org/10.1007/s10688-015-0116-x