$L^p$-Fourier analysis associated to a family of differential-reflection operators
Résumé
In a previous paper we introduced a family of differential-reflection operators
$\Lambda_{A, \varepsilon}$ acting on smooth functions defined on
$\mathbb R,$ where the spectral problem for the operators $\Lambda_{A, \varepsilon}$ has been discussed.
Here $A$ is a Sturm-Liouville function with additional hypotheses and $\varepsilon\in \mathbb R.$
Via the eigenfunctions of $\Lambda_{A,\varepsilon},$ we introduce in this paper a generalized Fourier
transform $\mathcal F_{A,\varepsilon}.$ An $L^p$-harmonic analysis for $\mathcal F_{A,\varepsilon}$ is
developed when $0< p \leq \frac{2}{1+\sqrt{1-\varepsilon^2}}$ and $-1\leq \varepsilon\leq 1.$
In particular, an $L^p$-Schwartz space isomorphism theorem for $\mathcal F_{A,\varepsilon}$ is proved.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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