✦ LIBER ✦

Interlacing properties of the zeros of the orthogonal polynomials and approximation of the Hilbert transform

✍ Scribed by G. Mastroianni; D. Occorsio

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 610 KB
Volume: 30
Category: Article
ISSN: 0898-1221
DOI: 10.1016/0898-1221(95)00093-3

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, starting from interlacing properties of the zeros of the orthogonai polynomials, the authors propose a new method to approximate the finite Hilbert transform. For this method they give error estimates in uniform norm.

📜 SIMILAR VOLUMES

The distribution of the zeros of certain

The distribution of the zeros of certain orthogonal polynomials

✍ A.McD Mercer 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 199 KB

The variation of zeros of certain orthog

The variation of zeros of certain orthogonal polynomials

✍ Mourad E.H Ismail 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 393 KB

Representations for the extreme zeros of

Representations for the extreme zeros of orthogonal polynomials

✍ Erik A. van Doorn; Nicky D. van Foreest; Alexander I. Zeifman 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 378 KB

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the de

Zeros of orthogonal polynomials on the r

Zeros of orthogonal polynomials on the real line

✍ Sergey A Denisov; Barry Simon 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 144 KB

Let p n ðxÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppðdmÞ; we show there is a d40 so that for all n; either p n or p nþ1 has no zeros in ðE À d; E þ dÞ: If E is an isolated point of suppðmÞ; we show there is a d so that for all n; either p n or p nþ

On the Zeros of Polynomials of Best Appr

On the Zeros of Polynomials of Best Approximation

✍ Thomas Bloom; Jerzy Szczepański 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 141 KB

Limits of zeros of orthogonal polynomial

Limits of zeros of orthogonal polynomials on the circle

✍ Barry Simon; Vilmos Totik 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 127 KB

## Abstract We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a qu