Boundary relations and generalized resolvents of symmetric operators View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-03

AUTHORS

V. Derkach, S. Hassi, M. Malamud, H. de Snoo

ABSTRACT

The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space extensions of a (not necessarily densely defined) symmetric operator in terms of maximal dissipative (in ℂ+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct generalized resolvents from given parameter families. A general version of the coupling method is introduced and the role of the boundary relations and their Weyl families in the Kreĭn-Naĭmark formula is investigated and explained. These notions lead to several new results and new types of solutions to problems involving generalized resolvents and their applications, e.g., in boundary-value problems for (ordinary and partial) differential operators. For instance, an old problem going back to M. A. Naĭmark and concerning the analytic characterization of the so-called Naĭmark extensions is solved. More... »

PAGES

17-60

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1061920809010026

DOI

http://dx.doi.org/10.1134/s1061920809010026

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020810486


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