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Mediterranean Journal of Mathematics

, Volume 2, Issue 3, pp 243–258 | Cite as

An Analogue of Beurling–Hörmander’s Theorem Associated with Partial Differential Operators

  • Lotfi Kamoun
  • Khalifa Trimèche
Original Paper

Abstract.

In this paper for a positive real number α we consider two partial differential operators D and Dα on the half–plane \(\mathbb{K} = [0, + \infty [ \times \mathbb{R}.\) We define a generalized Fourier transform \(\mathcal{F}_{\alpha } \) associated with the operators D and Dα. We establish an analogue of Beurling–Hörmander’s Theorem for this transform \(\mathcal{F}_{\alpha } \) and we give some applications of this theorem.

Mathematics Subject Classification (2000).

Primary 43A32 Secondary 42B10 

Keywords.

Generalized Fourier transform generalized Weyl integral transform Beurling–Hörmander’s Theorem. 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Sciences of MonastirMonastirTunisia
  2. 2.Department of MathematicsFaculty of Sciences of TunisTunisTunisia

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