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The Kontorovich–Lebedev Transform as a Map between d ‐Orthogonal Polynomials
Author(s) -
Ana F. Loureiro,
Semyon Yakubovich
Publication year - 2013
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12009
Subject(s) - orthogonal polynomials , mathematics , laguerre polynomials , classical orthogonal polynomials , hermite polynomials , discrete orthogonal polynomials , sequence (biology) , pure mathematics , hahn polynomials , jacobi polynomials , gegenbauer polynomials , mathematical analysis , genetics , biology
A slight modification of the Kontorovich–Lebedev transform is an auto‐morphism 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 to 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.