Turan inequalities and zeros of orthogonal polynomials

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Krasikov, Ilia
Format: Preprint
Published: 2004
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915560233631744
author Krasikov, Ilia
author_facet Krasikov, Ilia
contents We use Turan type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence $p_{k+1}=x p_k-c_k p_{k-1},$ with a nondecreasing sequence $\{c_k\}$. As a special case they include a non-asymptotic version of Mate, Nevai and Totik result on the largest zeros of orthogonal polynomials with $c_k=k^δ (1+ o(k^{-2/3})).$
format Preprint
id arxiv_https___arxiv_org_abs_math_0401299
institution arXiv
publishDate 2004
record_format arxiv
spellingShingle Turan inequalities and zeros of orthogonal polynomials
Krasikov, Ilia
Classical Analysis and ODEs
Numerical Analysis
33C45
We use Turan type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence $p_{k+1}=x p_k-c_k p_{k-1},$ with a nondecreasing sequence $\{c_k\}$. As a special case they include a non-asymptotic version of Mate, Nevai and Totik result on the largest zeros of orthogonal polynomials with $c_k=k^δ (1+ o(k^{-2/3})).$
title Turan inequalities and zeros of orthogonal polynomials
topic Classical Analysis and ODEs
Numerical Analysis
33C45
url https://arxiv.org/abs/math/0401299