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A support theorem for the Dunkl spherical mean operator


Author: Salem Ben Saïd
Journal: Proc. Amer. Math. Soc. 149 (2021), 279-284
MSC (2010): Primary 44A15; Secondary 39A70
DOI: https://doi.org/10.1090/proc/15206
Published electronically: October 16, 2020
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Abstract: We prove a support theorem for the Dunkl spherical mean operator. The proof relies on the decay of the total energy of the solutions to Euler-Poisson-Darboux type equations.


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Additional Information

Salem Ben Saïd
Affiliation: Mathematical Sciences Department, College of Science, United Arab Emirates University, Al Ain, United Arab Emirates
Email: salem.bensaid@uaeu.ac.ae

DOI: https://doi.org/10.1090/proc/15206
Keywords: Dunkl spherical mean operator, total energy, support theorem.
Received by editor(s): November 13, 2019
Received by editor(s) in revised form: May 25, 2020
Published electronically: October 16, 2020
Additional Notes: The author is thankful to United Arab Emirates University for the Start-up Grant No. G00002950.
Communicated by: Yuan Xu
Article copyright: © Copyright 2020 American Mathematical Society