EXTENDED RESOLVENTS AND EXTENDED SPECTRAL FUNCTIONS OF A HERMITIAN OPERATOR
Ju. L. Šmul′jan · Mathematics of the USSR-Sbornik · 1971
In this paper we construct the theory of extensions of Hermitian operators which are initially defined on a manifold in Hilbert space. The operators may have infinite defect numbers, and the manifold may fail to be dense. The extension is accompanied by a result in the Hilbert space of ideal elements (generalized functions which are defined on the Hilbert space of elements which belong to the basic Hilbert space: ). We conduct a detailed analysis of extended generalized resolvents and corresponding spectral functions. We explain the connection between functions of the form , where is an extended generalized resolvent, and the theory of -functions. Bibliography: 14 titles.