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2002 On connections between Hankel, Laguerre and Jacobi transplantations
Krzysztof Stempak
Tohoku Math. J. (2) 54(4): 471-493 (2002). DOI: 10.2748/tmj/1113247646

Abstract

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.

Citation

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Krzysztof Stempak. "On connections between Hankel, Laguerre and Jacobi transplantations." Tohoku Math. J. (2) 54 (4) 471 - 493, 2002. https://doi.org/10.2748/tmj/1113247646

Information

Published: 2002
First available in Project Euclid: 11 April 2005

zbMATH: 1040.42022
MathSciNet: MR1936265
Digital Object Identifier: 10.2748/tmj/1113247646

Subjects:
Primary: 42C10

Rights: Copyright © 2002 Tohoku University

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Vol.54 • No. 4 • 2002
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