Revisiting Beurling's theorem for Fourier–Dunkl transform

Abstract

We prove an analogue of Beurling's theorem in the setting of Fourier–Dunkl transform, which improves the theorem of Kawazoe–Mejjaoli [Uncertainty principles for the Dunkl transform. Hiroshima Math J. 2010;40(2):241–268].

Keywords:

• Beurling's theorem
• Dunkl kernel
• Fourier–Dunkl transform

2000 Mathematics Subject Classification:

• Primary: 33C80
• Secondary: 51F15
• 43A32

Disclosure statement

No potential conflict of interest was reported by the authors.