Rigidity of the Hamburger and Stieltjes moment sequences
Abstract
This paper aims at finding conditions on a Hamburger or Stieltjes moment sequence, under which the change of at most a finite number of its entries produces another sequence of the same type. It turns out that a moment sequence allows all small enough variations of this kind precisely when it is indeterminate. We also show that a determinate moment sequence has the finite index of determinacy if and only if the corresponding finite number of its entries can be changed in a certain way.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.00650
 arXiv:
 arXiv:1712.00650
 Bibcode:
 2017arXiv171200650D
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 30E05;
 44A60;
 42C05
 EPrint:
 13 pages