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Dunkl, C.F., Orthogonal polynomials of types A and B and related Calegero models, Commun. Math. Phys., 197. 451-487. 1998.

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Article

Oppenheim's Problem and Some Inequalities Involving Bessel Functions and Dunkl Kernels

1Department of Mathematics, University of Sousse, Higher School of Sciences and Technology of Hammam Sousse, 4011 Hammam Sousse, Tunisia


Turkish Journal of Analysis and Number Theory. 2018, Vol. 6 No. 3, 61-71
DOI: 10.12691/tjant-6-3-1
Copyright © 2018 Science and Education Publishing

Cite this paper:
Frej Chouchene. Oppenheim's Problem and Some Inequalities Involving Bessel Functions and Dunkl Kernels. Turkish Journal of Analysis and Number Theory. 2018; 6(3):61-71. doi: 10.12691/tjant-6-3-1.

Correspondence to: Frej  Chouchene, Department of Mathematics, University of Sousse, Higher School of Sciences and Technology of Hammam Sousse, 4011 Hammam Sousse, Tunisia. Email: frej.chouchene@essths.u-sousse.tn

Abstract

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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