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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Markov-type inequalities and extreme zeros of orthogonal polynomials

## Markov-type inequalities and extreme zeros of orthogonal polynomialsAdd to your list(s) Download to your calendar using vCal - Geno Nikolov (Sofia University St. Kliment Ohridski)
- Friday 21 June 2019, 14:20-15:10
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. ASCW03 - Approximation, sampling, and compression in high dimensional problems 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 $L_2$ 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 $L_2$ Markov inequalities with the Laguerre and Gegenbauer weight functions and in a discrete $\ell_2$ Markov-Bernstein inequality are investigated using the same tool. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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