On the range of the Fourier transform connected with Riemann-Liouville operator

Rachdi, Lakhdar Tannech; Rouz, Ahlem

Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 355-397.

We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator ${ℛ}_{\alpha },\alpha \ge 0$ and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.

Classification : 42B35, 43A32, 35S30
Mots clés : Riemann-Liouville operator, Fourier transform, Paley-Wiener-Schwartz theorems

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