The extension theory of Hermitian operators and the moment problem
This paper deals with the extension theory of a nondensely defined Hermitian operator in a Hilbert space. Generalized resolvents, preresolvent and resolvent matrices of such an operator are investigated. Necessary and sufficient conditions for a holomorphic operator-valued function to be a preresolvent or resolvent matrix of a Hermitian operator are found. A criterion for an \(R\)-function to be the Weyl function of a Hermitian operator is given. Applications to describe solutions of the truncated Hamburger, Stieltjes and Hausdorff moment problems are given. The results of this paper were partially announced in previous papers of the authors [Dokl. Akad. Nauk Ukr., Ser. A 11, 34-39 (1991); Dokl. Akad Nauk 323, No. 5, 816-822 (1992; Zbl 0820.47007); Dokl. Akad. Nauk 326, No. 1, 12-18 (1992)].
resolvent matrix of a Hermitian operator
truncated Hamburger, Stieltjes and Hausdorff moment problems
scientific article; zbMATH DE number 859204
scientific article