Abstract: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.
Keywords: Schrodinger operator, generalized eigenfunctions, generalized Fourier transforms, Paley-Wiener theorems
AMS Subject Classification: 47E05, 34B25