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A characterization of self-adjoint operators determined by the weak formulation of second-order singular differential expressions

EL-GEBEILY, MOHAMED
O'REGAN, DONAL
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Publication Date
2009-04-27
Type
Article
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Citation
EL-GEBEILY, MOHAMED; O'REGAN, DONAL (2009). A characterization of self-adjoint operators determined by the weak formulation of second-order singular differential expressions. Glasgow Mathematical Journal 51 , 385-404
Abstract
In this paper we describe a special class of self-adjoint operators associated with the singular self-adjoint second-order differential expression E. This class is defined by the requirement that the sesquilinear form q(u, v) obtained from e by integration by parts once agrees with the inner product < lu, v >. We call this class Type I operators. The Friedrichs Extension is a special case of these operators. A complete characterization of these operators is given, for the various values of the deficiency index, in terms of their domains and the boundary conditions they satisfy (separated or coupled).
Funder
Publisher
Cambridge University Press (CUP)
Publisher DOI
10.1017/s0017089509005060
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Attribution-NonCommercial-NoDerivs 3.0 Ireland