On the range of the generalized Fourier transform associated with a Cherednick type operator on the real line

Abstract

In this work, we establish the real Paley–Wiener theorem for the generalized Fourier transform on R. Therefore, we study the connection between the real Paley–Wiener theorem and local spectral theory. Finally, we generalize Roe’s theorem.

Keywords

• Cherednick type operator
• Real Paley–Wiener theorem
• Generalized Fourier transform
• Roe’s theorem