Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 54, Number 4 (2002), 471-493.
On connections between Hankel, Laguerre and Jacobi transplantations
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.
Tohoku Math. J. (2), Volume 54, Number 4 (2002), 471-493.
First available in Project Euclid: 11 April 2005
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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. https://projecteuclid.org/euclid.tmj/1113247646