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Spectral transformations of measures supported on the unit circle and the Szegő transformation

✍ Scribed by Luis Garza; Javier Hernández; Francisco Marcellán


Book ID
106487838
Publisher
Springer US
Year
2008
Tongue
English
Weight
374 KB
Volume
49
Category
Article
ISSN
1017-1398

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📜 SIMILAR VOLUMES


Szegő transformations and Nth order asso
✍ 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.

Orthogonal polynomials and measures on t
✍ L. Garza; J. Hernández; F. Marcellán 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 657 KB

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

Szegö polynomials and quadrature formula
✍ Leyla Daruis; Pablo González-Vera 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 354 KB

In this paper, computation of the so-called Szegö quadrature formulas is considered for some special weight functions on the unit circle. The case of the Lebesgue measure is more deeply analyzed. Illustrative numerical examples are also given.

Geronimus spectral transforms and measur
✍ F. Marcellán; J. Hernández 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 211 KB

We analyze a special spectral transform of a measure supported on a compact subset C of the complex plane. A perturbation 1 of is said to be a Geronimus spectral transform if d 1 = d |z -| 2 where / ∈ C. We focus our attention in the analysis of the Hessenberg matrix associated with the multiplicati