## Tokyo Journal of Mathematics

### Fractional Calculus and Analytic Continuation of the Complex Fourier-Jacobi Transform

#### Abstract

By using the Riemann-Liouville type fractional integral operators we shall reduce the complex Fourier-Jacobi transforms of even functions on $\mathbf{R}$ 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 $C^\infty$ and not compactly supported on $\mathbf{R},$ whose transforms have meromorphic extensions on the upper half plane.

#### Article information

Source
Tokyo J. Math., Volume 27, Number 1 (2004), 187-207.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208484

Digital Object Identifier
doi:10.3836/tjm/1244208484

Mathematical Reviews number (MathSciNet)
MR2060084

Zentralblatt MATH identifier
1087.42001

#### Citation

KAWAZOE, Takeshi; LIU, Jianming. Fractional Calculus and Analytic Continuation of the Complex Fourier-Jacobi Transform. Tokyo J. Math. 27 (2004), no. 1, 187--207. doi:10.3836/tjm/1244208484. https://projecteuclid.org/euclid.tjm/1244208484