A distribution framework for the generalized Fourier transform associated with a Sturm--Liouville operator

Christophe Hazard 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : The generalized Fourier transform associated with a selfadjoint Sturm--Liouville operator is a unitary transformation which converts the action of this operator into a simple product by a spectral variable. For a particular operator defined on the half-line and which involves a step function, we show how to extend such a transformation to generalized functions, or distributions, with a suitable definition of such distributions. This extension is based essentially on the fact that, as the usual Fourier transform, this transformation has the property to exchange regularity and decay between the physical and spectral variables.
Document type :
Reports
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

https://hal.inria.fr/inria-00371350
Contributor : Christophe Hazard <>
Submitted on : Friday, March 27, 2009 - 3:15:41 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM
Long-term archiving on : Thursday, June 10, 2010 - 6:59:36 PM

File

RR-6885.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00371350, version 1

Collections

Citation

Christophe Hazard. A distribution framework for the generalized Fourier transform associated with a Sturm--Liouville operator. [Research Report] RR-6885, INRIA. 2009, pp.18. ⟨inria-00371350⟩

Share

Metrics

Record views

409

Files downloads

245