Fractional calculus and analytic continuation of the complex fourier-jacobi transform

Takeshi Kawazoe, Liu Jianming

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)187-207
Number of pages21
JournalTokyo Journal of Mathematics
Volume27
Issue number1
DOIs
Publication statusPublished - 2004 Jan 1

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Fractional Calculus
Analytic Continuation
Jacobi
Even function
Transform
Reduction formula
Fractional Integral Operator
Inversion Formula
Meromorphic
Half-plane
Fourier transform
Euclidean

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fractional calculus and analytic continuation of the complex fourier-jacobi transform. / Kawazoe, Takeshi; Jianming, Liu.

In: Tokyo Journal of Mathematics, Vol. 27, No. 1, 01.01.2004, p. 187-207.

Research output: Contribution to journalArticle

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