Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line

Abstract

We give an elementary proof of the Paley-Wiener theorem for smooth functions for the Dunkl transforms on the real line, establish a similar theorem for L^2-functions and prove identities in the spirit of Bang for L^p-functions. The proofs seem to be new also in the special case of the Fourier transform.

9 pp., LaTeX, no figures; final version, to appear in Int. Math. Res. Not

References in corpus (1)

• Paley-Wiener theorems for the Dunkl transform

Cited by in corpus (4)

• Real Paley-Wiener theorems and local spectral radius formulas
• Bilinear biorthogonal expansions and the Dunkl kernel on the real line
• Mean convergence of Fourier-Dunkl series
• Uncertainty principles for eventually constant sign bandlimited functions