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arXiv · 1206.4899

The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials

Ana F. Loureiro·S. Yakubovich
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Abstract

A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this $KL_α$-transform over certain polynomial sequences will be under discussion, and a special attention will be given the d-orthogonal ones. For instance, the Continuous Dual Hahn polynomials appear as the $KL_α$-transform of a 2-orthogonal sequence of Laguerre type. Finally, all the orthogonal polynomial sequences whose $KL_α$-transform is a $d$-orthogonal sequence will be characterized: they are essencially semiclassical polynomials fulfilling particular conditions and $d$ is even. The Hermite and Laguerre polynomials are the classical solutions to this problem.

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BibTeXRIS

Ana F. Loureiro, S. Yakubovich. 2012-06-21. The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials. https://arxiv.org/abs/1206.4899

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