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

Lakhdar Tannech Rachdi[1]; Ahlem Rouz[1]

  • [1] Department of Mathematics Faculty of Sciences of Tunis 2092 El Manar 2 Tunis Tunisia

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 2, page 355-397
  • ISSN: 1259-1734

Abstract

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We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator ℛ α , α ≥ 0 and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.

How to cite

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Rachdi, Lakhdar Tannech, and Rouz, Ahlem. "On the range of the Fourier transform connected with Riemann-Liouville operator." Annales mathématiques Blaise Pascal 16.2 (2009): 355-397. <http://eudml.org/doc/10585>.

@article{Rachdi2009,
abstract = {We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator $\mathscr\{R\}_\{\alpha \},\ \alpha \ge 0$ and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.},
affiliation = {Department of Mathematics Faculty of Sciences of Tunis 2092 El Manar 2 Tunis Tunisia; Department of Mathematics Faculty of Sciences of Tunis 2092 El Manar 2 Tunis Tunisia},
author = {Rachdi, Lakhdar Tannech, Rouz, Ahlem},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Riemann-Liouville operator; Fourier transform; Paley-Wiener-Schwartz theorems},
language = {eng},
month = {7},
number = {2},
pages = {355-397},
publisher = {Annales mathématiques Blaise Pascal},
title = {On the range of the Fourier transform connected with Riemann-Liouville operator},
url = {http://eudml.org/doc/10585},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Rachdi, Lakhdar Tannech
AU - Rouz, Ahlem
TI - On the range of the Fourier transform connected with Riemann-Liouville operator
JO - Annales mathématiques Blaise Pascal
DA - 2009/7//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 2
SP - 355
EP - 397
AB - We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator $\mathscr{R}_{\alpha },\ \alpha \ge 0$ and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.
LA - eng
KW - Riemann-Liouville operator; Fourier transform; Paley-Wiener-Schwartz theorems
UR - http://eudml.org/doc/10585
ER -

References

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