Markov-type inequalities and extreme zeros of orthogonal polynomials
Duration: 50 mins 18 secs
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About this item
| Description: |
Nikolov, G
Friday 21st June 2019 - 14:20 to 15:10 |
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| Created: | 2019-06-21 15:38 |
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| Collection: | Approximation, sampling, and compression in high dimensional problems |
| Publisher: | Isaac Newton Institute |
| Copyright: | Nikolov, G |
| Language: | eng (English) |
| Abstract: | The talk is centered around the problem of finding (obtaining tight two-sided bounds for) the sharp constants in certain Markov-Bernstein type inequalities in weighted L2 norms. It turns out that, under certain assumptions, this problem is equivalent to the estimation of the extreme zeros of orthogonal polynomials with respect to a measure supported on R+. It will be shown how classical tools like the Euler-Rayleigh method and Gershgorin circle theorem produce surprisingly good bounds for the extreme zeros of the Jacobi, Gegenbauer and Laguerre polynomials. The sharp constants in the L2 Markov inequalities with the Laguerre and Gegenbauer weight functions and in a discrete ℓ2 Markov-Bernstein inequality are investigated using the same tool. |
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