A family of pseudo-differential operators on the Schwartz space associated with the fractional Fourier transform

DOI10.1134/S1061920817040124zbMath1387.35645OpenAlexW2771960186MaRDI QIDQ1702425

Santosh Kumar Upadhyay, Hari M. Srivastava, Komal Khatterwani

Publication date: 28 February 2018

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920817040124

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (13)

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space ⋮ Product of pseudo-differential operators associated with zero order Mehler-Fock transform ⋮ Pseudo-differential operators associated with modified fractional derivatives involving the fractional Fourier transform ⋮ The generalized Kontorovich-Lebedev transform and associated operators ⋮ Pseudo‐differential operator in quaternion space ⋮ Multidimensional fractional wavelet transforms and uncertainty principles ⋮ A framework of linear canonical Hankel transform pairs in distribution spaces and their applications ⋮ Abelian theorems and Calderón's reproducing formula for linear canonical wavelet transform ⋮ \(L_{\alpha }^p\)-boundedness of the pseudo-differential operators associated with the Kontorovich-Lebedev transform ⋮ Pseudo-differential type operators and Gevrey spaces ⋮ Continuous wavelet transform of Schwartz tempered distributions in \(S^\prime (\mathbb{R}^n)\) ⋮ Continuous wavelet transform involving canonical convolution ⋮ Boundedness of integral operators associated with the Kontorovich–Lebedev transform in the Lebesgue spaces type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Opérateurs pseudo-différentiels analytiques et opérateurs d'ordre infini. (Analytic pseudo-differential operators and operators of infinite order.)
• Fractional Fourier transform in the framework of fractional calculus operators
• Gelfand-Shilov Spaces, Pseudo-differential Operators and Localization Operators
• Pseudodifferential operators of infinite order and Gevrey classes
• The Curious History of Faa di Bruno's Formula
• An Introduction to Pseudo-Differential Operators
• An algebra of pseudo‐differential operators

This page was built for publication: A family of pseudo-differential operators on the Schwartz space associated with the fractional Fourier transform