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Keywords:
Schrodinger operator; generalized eigenfunctions; generalized Fourier transforms; Paley-Wiener theorems
Schrodinger operator; generalized eigenfunctions; generalized Fourier transforms; Paley-Wiener theorems
Summary:
In this paper we define and study generalized Fourier transforms associated with some class of Schrodinger operators on $\Bbb R$. Next, we establish Paley-Wiener type theorems which characterize some functional spaces by their generalized Fourier transforms.
References:
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[4] Faraut J.: Décomposition spectrale de l'opérateur de Schrodinger et matrice de diffusion. Séminaire d'analyse harmonique de Tunis, Exposé no. 20, Juin 1979.
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[6] Titchmarch E.C.: Eigenfunction Expansion Associated with the Second Order Differential Equations. Oxford-Clarendon Press, 1948.
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