A Formula and Sharp Estimates for the Dunkl Kernel for the Root System A2
Journal of Lie TheoryIn this paper, we transform a formula for the $A_2$ Dunkl kernel by Béchir Amri. The resulting formula expresses the $A_2$ Dunkl kernel in terms of the $A_1$ Dunkl kernel involving only positive terms. This result allows us to derive sharp estimates for the $A_2$ Dunkl kernel.
Graczyk, Piotr, Sawyer, Patrice
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Oppenheim's Problem and Some Inequalities Involving Bessel Functions and Dunkl Kernels [PDF]
Turkish Journal of Analysis and Number Theory, 2018 In this paper, we establish some inequalities related to Oppenheim's problem for the real and imaginary parts of Dunkl kernels In order to prove our main results, we present some new inequalities involving Bessel functions of the first kind. Refinements of inequalities for Bessel functions are also given.
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Optimal bounds for the Dunkl kernel in the dihedral case
Journal of Functional AnalysisWe establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
Anker, Jean-Philippe, Trojan, Bartosz
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Pitt's inequalities and uncertainty principle for generalized Fourier transform
, 2015 We study the two-parameter family of unitary operators \[ \mathcal{F}_{k,a}=\exp\Bigl(\frac{i\pi}{2a}\,(2\langle k\rangle+{d}+a-2 )\Bigr) \exp\Bigl(\frac{i\pi}{2a}\,\Delta_{k,a}\Bigr), \] which are called $(k,a)$-generalized Fourier transforms and ...
Gorbachev, Dmitry +2 more
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Paley-Wiener theorems for the Dunkl transform
, 2005 We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra.
de Jeu, Marcel
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Approaching Bilinear Multipliers via a Functional Calculus. [PDF]
J Geom Anal, 2018 Wróbel B.
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A Refinement of the Robertson-Schrödinger Uncertainty Principle and a Hirschman-Shannon Inequality for Wigner Distributions. [PDF]
J Fourier Anal Appl, 2019 Dias NC, de Gosson MA, Prata JN.
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Locally learning biomedical data using diffusion frames. [PDF]
J Comput Biol, 2012 Ehler M, Filbir F, Mhaskar HN.
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An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection. [PDF]
Theor Popul Biol, 2013 Steinrücken M, Wang YX, Song YS.
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The Z(2)(n) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra [PDF]
, 2016 De Bie, Hendrik +2 more
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