Tur\'an Type Inequalities for Dunkl Kernel and $q$-Dunkl Kernel
Khaled Mehrez, Mariem Ben Said, Jamel El Kamel
TL;DR
This paper establishes Turán type inequalities for Dunkl and q-Dunkl kernels, introduces a q-integral representation, and employs a q-Schwartz inequality to derive new bounds, advancing the understanding of these special functions.
Contribution
It provides the first Turán inequalities for Dunkl kernels and introduces a q-integral representation, connecting these kernels with q-analogs and inequalities.
Findings
Proved Turán inequalities for Dunkl kernel.
Derived a q-integral representation for q-Dunkl kernel.
Established Turán inequalities for q-Dunkl kernel using q-Schwartz inequality.
Abstract
We prove tur\'an type inequalities for Dunkl kernel. We provide a -integral representation for the -Dunkl kernel. Using a -version of Schwartz inequality, we get a tur\'an type inequalities for -Dunkl kernel.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Numerical methods in inverse problems