A unified class of integral transforms related to the Dunkl transform

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• 作者：Sami Ghazouani^a ; ^{Sami.Ghazouani@ipeib.rnu.tn} ; El Amine Soltani^b ; ^{aminesoltani@hotmail.fr} ; Ahmed Fitouhi^a ; ^{Ahmed.Fitouhi@fst.rnu.tn}
• 关键词：Canonical commutation relation ; Dunkl transform ; Fractional Dunkl transform ; Generalized Hermite polynomials and functions ; Semigroups of operators
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1797-1849
• 全文大小：750 K
• 卷排序：449

文摘

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 Dunkl transform, Dunkl transform, linear canonical transform, canonical Hankel 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.