On connections between Hankel, Laguerre and Jacobi transplantations

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概要

• 論文の詳細を見る

• 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 $α,γ>-1$ 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 $α,γ\ge-1/2$ the same is obtained by using Schindler's explicit kernel formula for the transplantation operator.

• 東北大学の論文

著者

• Stempak Krzysztof

  Institut Matematyki Politechnikawroclawska

関連論文

• On connections between Hankel, Laguerre and Jacobi transplantations
• Conjugate expansions for ultraspherical functions
• Addendum: Conjugate expansions for ultraspherical functions
• Heat-diffusion and Poisson integrals for Laguerre expansions

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