The Range of the Spectral Projection Associated with the Dunkl Laplacian

Salem Ben Said, Hatem Mejjaoli

Research output: Contribution to journalArticlepeer-review

Abstract

For s∈ℝ, denote by Pksf the "projection"of a function f in Dℝd into the eigenspaces of the Dunkl Laplacian Δk corresponding to the eigenvalue -s2. The parameter k comes from Dunkl's theory of differential-difference operators. We shall characterize the range of Pks on the space of functions f∈Dℝd supported inside the closed ball BO,R¯. As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform.

Original languageEnglish
Article number7803719
JournalJournal of Function Spaces
Volume2020
DOIs
Publication statusPublished - 2020

ASJC Scopus subject areas

  • Analysis

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