Geodesic
A CHARACTERIZATION OF SELF-ADJOINT OPERATORS DETERMINED BY THE WEAK FORMULATION OF SECOND-ORDER SINGULAR DIFFERENTIAL EXPRESSIONS
Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 385-404

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DOI

In this paper we describe a special class of self-adjoint operators associated with the singular self-adjoint second-order differential expression l. This class is defined by the requirement that the sesquilinear form q(u, v) obtained from l 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).
DOI : 10.1017/S0017089509005060
Mots-clés : 34B15, 34A34 
EL-GEBEILY, MOHAMED; O'REGAN, DONAL. A CHARACTERIZATION OF SELF-ADJOINT OPERATORS DETERMINED BY THE WEAK FORMULATION OF SECOND-ORDER SINGULAR DIFFERENTIAL EXPRESSIONS. Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 385-404. doi: 10.1017/S0017089509005060
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     title = {A {CHARACTERIZATION} {OF} {SELF-ADJOINT} {OPERATORS} {DETERMINED} {BY} {THE} {WEAK} {FORMULATION} {OF} {SECOND-ORDER} {SINGULAR} {DIFFERENTIAL} {EXPRESSIONS}},
     journal = {Glasgow mathematical journal},
     pages = {385--404},
     year = {2009},
     volume = {51},
     number = {2},
     doi = {10.1017/S0017089509005060},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509005060/}
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