Geodesic
Extended resolvents and extended spectral functions of a Hermitian operator
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 435-450 
Yu. L. Shmul'yan. Extended resolvents and extended spectral functions of a Hermitian operator. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 435-450. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a6/
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     title = {Extended resolvents and extended spectral functions of {a~Hermitian} operator},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\mathfrak H_-$ of ideal elements (generalized functions which are defined on the Hilbert space of elements which belong to the basic Hilbert space: $\mathfrak H_+\subset\mathfrak H$). We conduct a detailed analysis of extended generalized resolvents and corresponding spectral functions. We explain the connection between functions of the form $(\widehat R_\lambda f, f)$, where $\widehat R_\lambda$ is an extended generalized resolvent, and the theory of $R$-functions. Bibliography: 14 titles.

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