We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
Mots clés : Riemann-Liouville operator, Fourier transform, Paley-Wiener-Schwartz theorems
Lakhdar Tannech Rachdi 1 ; Ahlem Rouz 1
@article{AMBP_2009__16_2_355_0, author = {Lakhdar Tannech Rachdi and Ahlem Rouz}, title = {On the range of the {Fourier} transform connected with {Riemann-Liouville} operator}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {355--397}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {16}, number = {2}, year = {2009}, doi = {10.5802/ambp.272}, mrnumber = {2568871}, zbl = {1179.42019}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.272/} }
TY - JOUR AU - Lakhdar Tannech Rachdi AU - Ahlem Rouz TI - On the range of the Fourier transform connected with Riemann-Liouville operator JO - Annales mathématiques Blaise Pascal PY - 2009 SP - 355 EP - 397 VL - 16 IS - 2 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.272/ DO - 10.5802/ambp.272 LA - en ID - AMBP_2009__16_2_355_0 ER -
%0 Journal Article %A Lakhdar Tannech Rachdi %A Ahlem Rouz %T On the range of the Fourier transform connected with Riemann-Liouville operator %J Annales mathématiques Blaise Pascal %D 2009 %P 355-397 %V 16 %N 2 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.272/ %R 10.5802/ambp.272 %G en %F AMBP_2009__16_2_355_0
Lakhdar Tannech Rachdi; Ahlem Rouz. On the range of the Fourier transform connected with Riemann-Liouville operator. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 2, pp. 355-397. doi : 10.5802/ambp.272. https://ambp.centre-mersenne.org/articles/10.5802/ambp.272/
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