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.
@article{119002, author = {Mohamed N\'ejib Lazhari}, title = {Paley-Wiener theorems for the Schrodinger operator on $\Bbb R$}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {39}, year = {1998}, pages = {227-235}, zbl = {0937.47050}, mrnumber = {1651934}, language = {en}, url = {http://dml.mathdoc.fr/item/119002} }
Lazhari, Mohamed Néjib. Paley-Wiener theorems for the Schrodinger operator on $\Bbb R$. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 227-235. http://gdmltest.u-ga.fr/item/119002/
Inverse problem of scattering theory (in Russian), K.G.U. Karkov, 1960.
La matrice de scattering pour l'operateur de Schrodinger sur la droite réelle, Séminaire N. Bourbaki, 32e anné, Exposé no. 557, Juin 1980, p. 557-01 à 557-11.
Inverse problem of quantum scattering theory, J. Soviet Math. 5 (1976), 335-395. (1976) | Zbl 0373.35014
Décomposition spectrale de l'opérateur de Schrodinger et matrice de diffusion, Séminaire d'analyse harmonique de Tunis, Exposé no. 20, Juin 1979.
Integral Equation and their Application, first edition, vol. 1, pp. 8-13, Pergamon Press, 1966. | MR 0201934
Eigenfunction Expansion Associated with the Second Order Differential Equations, Oxford-Clarendon Press, 1948.