TY - JOUR
T1 - Fractional calculus and analytic continuation of the complex fourier-jacobi transform
AU - Takeshi, Kawazoe
AU - Jianming, Liu
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
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U2 - 10.3836/tjm/1244208484
DO - 10.3836/tjm/1244208484
M3 - Article
AN - SCOPUS:85024751956
SN - 0387-3870
VL - 27
SP - 187
EP - 207
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 1
ER -