Arkiv för Matematik

  • Ark. Mat.
  • Volume 17, Number 1-2 (1979), 139-151.

Jacobi functions: The addition formula and the positivity of the dual convolution structure

Mogens Flensted-Jensen and Tom H. Koornwinder

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We prove an addition formula for Jacobi functions $\varphi _\lambda ^{\left( {\alpha ,\beta } \right)} \left( {\alpha \geqq \beta \geqq - \tfrac{1}{2}} \right)$ analogous to the known addition formula for Jacobi polynomials. We exploit the positivity of the coefficients in the addition formula by giving the following application. We prove that the product of two Jacobi functions of the same argument has a nonnegative Fourier-Jacobi transform. This implies that the convolution structure associated to the inverse Fourier-Jacobi transform is positive.


The first author was partially supported by the Danish Natural Science Research Council.

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Ark. Mat., Volume 17, Number 1-2 (1979), 139-151.

Received: 17 July 1978
First available in Project Euclid: 31 January 2017

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1979 © Institut Mittag-Leffler


Flensted-Jensen, Mogens; Koornwinder, Tom H. Jacobi functions: The addition formula and the positivity of the dual convolution structure. Ark. Mat. 17 (1979), no. 1-2, 139--151. doi:10.1007/BF02385463.

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