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Orthogonal polynomials and cubic transformations

✍ Scribed by Francisco Marcellán; Gabriela Sansigre


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
519 KB
Volume
49
Category
Article
ISSN
0377-0427

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Let D and E be two real intervals. We consider transformations that map polynomials with zeros in D into polynomials with zeros in E. A general technique for the derivation of such transformations is presented. It is based on identifying the transformation with a parametrised distribution ~(x,/~), x

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In this paper we analyze a perturbation of a nontrivial positive measure supported on the unit circle. This perturbation is the inverse of the Christoffel transformation and is called the Geronimus transformation. We study the corresponding sequences of monic orthogonal polynomials as well as the co