A unified class of integral transforms related to the Dunkl transform

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Ghazouani, Sand¹  Soltani, El Amine²  Fitouhi, Ahmed¹ 

[1] Univ Tunis El Manar, Fac Sci Tunis, Tunis 2092, Tunisia

[2] Univ Carthage, Inst Preparatoire Etud Ingenieur Bizerte, Jarzouna 7021, Tunisia

关键词: Canonical commutation relation;    Dunkl transform;    Fractional Dunkl transform;    Generalized Hermite polynomials and functions;    Semigroups of operators;   

DOI  :  10.1016/j.jmaa.2016.12.054

来源: Elsevier

【 摘 要 】

In the present paper, a new family of integral transforms depending on two parameters and related to the Dunkl transform is introduced. Well-known transforms, such as the fractional Dunki transform, Dunkl transform, linear canonical transform, canonical Henkel transform, Fresnel transform, etc., can be seen to be special cases of this general transform. Some useful properties of the considered transform such as Riemann Lebesgue lemma, reversibility property, additivity property, operational formula, Plancherel formula, Bochner type identity and master formula are derived. The intimate connection that exists between this transformation and the quantum harmonic oscillator is developed. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free