Tohoku Mathematical Journal

On connections between Hankel, Laguerre and Jacobi transplantations

Krzysztof Stempak

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Proved are two results showing connections between the Hankel transplantation and a transplantation for a certain kind of Laguerre and Jacobi expansions. An asymptotic formula of Hilb's type for Laguerre and Jacobi polynomials is used. As an application of this link we obtain an extension of Guy's transplantation theorem for the Hankel transform to the case $\alpha,\gamma>-1$ also with more weights allowed. This is done by transferring a corresponding transplantation result for Jacobi expansions which was proved by Muckenhoupt. In the case when $\alpha,\gamma\ge-1/2$ the same is obtained by using Schindler's explicit kernel formula for the transplantation operator.

Article information

Tohoku Math. J. (2), Volume 54, Number 4 (2002), 471-493.

First available in Project Euclid: 11 April 2005

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Zentralblatt MATH identifier

Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Hankel transformation transplantation Laguerre and Jacobi expansions


Stempak, Krzysztof. On connections between Hankel, Laguerre and Jacobi transplantations. Tohoku Math. J. (2) 54 (2002), no. 4, 471--493. doi:10.2748/tmj/1113247646.

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