GAMP seminar by Alexander Dyachenko
Seminar by Alexander Dyachenko, Keldysh Institute of applied mathematics (RAS)
The classical moment problems by Stieltjes and Hamburger consist in finding a distribution of masses (positive measure) over the real line based on a sequence of the moments. Alteration of the mass at the origin only changes the leading moment, while the other moments remain fixed. This talk is devoted to the related question motivated by combinatorics: when can we perturb a finite number of moments so that the sequence keeps being generated by some positive measure?
It turns out that the relevant conditions on the leading moments can be expressed through polynomial inequalities. In particular, a Hamburger (or Stieltjes) moment sequence allows all small enough perturbations of this kind precisely when the moment problem is indeterminate. Certain perturbations of this kind are also possible for determinate moment problems if the so-called index of determinacy is finite.