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Szegő transformations and rational spectral transformations for associated polynomials

✍ Scribed by L. Garza; F. Marcellán

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
495 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this contribution we analyze rational spectral transformations related to associated polynomials with respect to probability measures supported on the interval [-1, 1]. The connection with rational spectral transformations of measures supported on the unit circle using the Szegő transformation is presented.

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Szegő transformations and Nth order associated polynomials on the unit circle
✍ L. Garza; F. Marcellán 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 641 KB

In this paper we analyze the Stieltjes functions defined by the Szegő inverse transformation of a nontrivial probability measure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their Verblunsky parameters.