Geodesic
On Invertible Contractions of Quotients Generated by a Differential Expression and by a Nonnegative Operator Function
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 652-664

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In the present paper, we describe invertible contractions of the maximal quotient generated by a differential expression with bounded operator coefficients and by a nonnegative operator function. We show that the operators inverse to such contractions are integral operators and prove a criterion for such operators to be holomorphic. Using the results obtained, we describe the generalized resolvents of symmetric quotients.
Mots-clés : invertible contraction
Keywords: integral operator, holomorphic operator, operator function, Hilbert space, self-adjoint operator, Borel measurable function. 
@article{MZM_2007_82_5_a1,
     author = {V. M. Bruk},
     title = {On {Invertible} {Contractions} of {Quotients} {Generated} by a {Differential} {Expression} and by a {Nonnegative} {Operator} {Function}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {652--664},
     publisher = {mathdoc},
     volume = {82},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a1/}
}
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V. M. Bruk. On Invertible Contractions of Quotients Generated by a Differential Expression and by a Nonnegative Operator Function. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 652-664. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a1/