TY - JOUR
T1 - The Range of the Spectral Projection Associated with the Dunkl Laplacian
AU - Ben Said, Salem
AU - Mejjaoli, Hatem
N1 - Funding Information:
S. Ben Said would like to thankfully acknowledge the financial support awarded by UAEU through the Start-up grant. No. G00002950.
Publisher Copyright:
© 2020 Salem Ben Said and Hatem Mejjaoli.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.1155/2020/7803719
DO - 10.1155/2020/7803719
M3 - Article
AN - SCOPUS:85089347837
SN - 2314-8896
VL - 2020
JO - Journal of Function Spaces
JF - Journal of Function Spaces
M1 - 7803719
ER -