Abstract
In this survey article we overview transplantation theorems for several types of continuous and discrete orthogonal expansions. These include: Hankel and Dunkl transforms, and Fourier-Bessel, Jacobi and Laguerre expansions. We also discuss the idea of transference of transplantation and point out how a notion of conjugacy for orthogonal expansions may be interpreted as a generalized transplantation.
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Communicated by P.L. Butzer.
Dedicated to Professor Paul Leo Butzer on the occasion of his 80th birthday.
This article is an extended version of the talk given by the author on the conference Approximation Theory and Signal Analysis, Lindau, Germany, March 21–24, 2009.
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Stempak, K. Transplantation Theorems—A Survey. J Fourier Anal Appl 17, 408–430 (2011). https://doi.org/10.1007/s00041-010-9130-9
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DOI: https://doi.org/10.1007/s00041-010-9130-9
Keywords
- Transplantation
- Hankel transform
- Dunkl transform
- Fourier-Bessel expansions
- Jacobi expansions
- Laguerre expansions
- Transference
- Conjugacy