Geodesic
On characteristic functions of generalized resolvents generated by integral equations with operator measures
Filomat, Tome 37 (2023) no. 23, p. 7699

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DOI

We consider a symmetric minimal relation L 0 generated by an integral equation with operators measures. We describe the generalized resolvents of L 0 using the characteristic function M(λ) (λ ∈ C), i.e., a function that has the property (Imλ) −1 ImM(λ) ⩾ 0. We obtain a necessary and sufficient condition for a holomorphic function M(λ) to be a characteristic function of a generalized resolvent. We give a detailed example of finding the characteristic function.
DOI : 10.2298/FIL2323699B
Classification : 47A10, 47B25, 45N05
Keywords: Hilbert space, integral equation, operator measure, linear relation, symmetric relation, generalized resolvent 
Vladislav M Bruk. On characteristic functions of generalized resolvents generated by integral equations with operator measures. Filomat, Tome 37 (2023) no. 23, p. 7699 . doi: 10.2298/FIL2323699B
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     title = {On characteristic functions of generalized resolvents generated by integral equations with operator measures},
     journal = {Filomat},
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     year = {2023},
     volume = {37},
     number = {23},
     doi = {10.2298/FIL2323699B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323699B/}
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