Geodesic
Linear relations generated by an integral equation with Nevanlinna operator measure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 3-19

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We define families of maximal and minimal linear relations generated by an integral equation with Nevanlinna operator measure and prove their holomorphic property. We also prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We apply the obtained results for proving the constancy of deficient numbers of some integral and differential equations.
Keywords: Hilbert space, linear relation, integral equation, holomorphic family of relations, deficient number. 
@article{IVM_2012_10_a0,
     author = {V. M. Bruk},
     title = {Linear relations generated by an integral equation with {Nevanlinna} operator measure},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--19},
     publisher = {mathdoc},
     number = {10},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_10_a0/}
}
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V. M. Bruk. Linear relations generated by an integral equation with Nevanlinna operator measure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 3-19. http://geodesic.mathdoc.fr/item/IVM_2012_10_a0/