The two-sided quaternionic Dunkl transform and Hardy's theorem

DOI10.1007/S12215-021-00708-5OpenAlexW4205629229MaRDI QIDQ2687375

Saïd Fahlaoui, Mohamed Essenhajy

Publication date: 2 March 2023

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12215-021-00708-5

zbMATH Keywords

quaternionic analysisHardy's theoremuncertainty principlesDunkl transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions associated with root systems (33C52) Abstract harmonic analysis (43-XX) Harmonic analysis on Euclidean spaces (42-XX)

Cites Work

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• Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem
• The Dunkl transform
• An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups
• Connecting spatial and frequency domains for the quaternion Fourier transform
• Exact operator solution of the Calogero-Sutherland model
• Positivity of Dunkl's intertwining operator
• Convolution products for hypercomplex Fourier transforms
• Quaternion and Clifford Fourier Transforms and Wavelets
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• An L^P version of Hardy's theorem for the Dunkl transform
• Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis

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