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SUMMARY:Markov-type inequalities and extreme zeros of orthogonal polynomia
 ls - Geno Nikolov  (Sofia University St. Kliment Ohridski)
DTSTART:20190621T132000Z
DTEND:20190621T141000Z
UID:TALK126328@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The talk is centered around the problem of finding (obtaining&
 nbsp\; tight two-sided bounds for)&nbsp\; the sharp constants in certain M
 arkov-Bernstein type inequalities in weighted $L_2$ norms. It turns out th
 at\, under certain assumptions\, this problem is equivalent to the estimat
 ion of the extreme zeros of orthogonal polynomials with respect to a measu
 re supported on $R_{+}$.  It will be shown how classical tools like the Eu
 ler-Rayleigh method and Gershgorin circle theorem produce surprisingly goo
 d bounds for the extreme zeros of the Jacobi\, Gegenbauer and Laguerre pol
 ynomials. The sharp constants in the $L_2$&nbsp\; Markov inequalities with
  the Laguerre and Gegenbauer weight functions and in a discrete $\\ell_2$ 
 Markov-Bernstein inequality are investigated using the same tool.
LOCATION:Seminar Room 1\, Newton Institute
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