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TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE
Journal article   Peer reviewed

TRANSMUTATION OPERATORS AND PALEY–WIENER THEOREM ASSOCIATED WITH A CHEREDNIK TYPE OPERATOR ON THE REAL LINE

MOHAMED ALI Mourou
Analysis and applications, Vol.8(4), pp.387-408
10/2010
DOI: https://doi.org/10.1142/S0219530510001692

Abstract

generalized convolution transmutation operators Paley–Wiener theorem Differential-difference operators
We consider a singular differential-difference operator Λ on the real line which generalizes the one-dimensional Cherednik operator. We construct transmutation operators between Λ and first-order regular differential-difference operators on ℝ. We exploit these transmutation operators, firstly to establish a Paley–Wiener theorem for the Fourier transform associated with Λ, and secondly to introduce a generalized convolution on ℝ tied to Λ.

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