By using the Riemann-Liouville type fractional integral operators we shall reduce the complex Fourier-Jacobi transforms of even functions on R to the Euclidean Fourier transforms. As an application of the reduction formula, Parseval’s formula and an inversion formula of the complex Jacobi transform are easily obtained. Moreover, we shall introduce a class of even functions, not C∞ and not compactly supported on R, whose transforms have meromorphic extensions on the upper half plane.
ASJC Scopus subject areas
- 数学 (全般)