Geometric and operator measures of degeneracy for the set of solutions to the Stieltjes matrix moment problem

Yu. M. Dyukarev

Sbornik. Mathematics, Tome 207 (2016) no. 4, pp. 519-536

Résumé

The ranks of the limit Weyl intervals are known to serve as the geometric measure of degeneracy of the solution set to a Stieltjes matrix moment problem. This paper puts forward the first operator measure of degeneracy for the solution set to a Stieltjes matrix moment problem in terms of the deficiency vectors of a pair of associated positive symmetric operators. A relationship between the geometric and operator measures of degeneracy for a Stieltjes matrix moment problem is established, from which some corollaries about the Stieltjes matrix moment problem are obtained. Bibliography 19 titles.

Détail

Keywords: Weyl intervals, Weyl discs, symmetric operators, deficiency vectors.
Mots-clés : the Stieltjes matrix moment problem

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