Turan inequalities and zeros of orthogonal polynomials
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arXiv
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| Format: | Preprint |
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2004
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| _version_ | 1866915560233631744 |
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| 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 |
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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 |