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A CHARACTERIZATION OF SELF-ADJOINT OPERATORS DETERMINED BY THE WEAK FORMULATION OF SECOND-ORDER SINGULAR DIFFERENTIAL EXPRESSIONS

Published online by Cambridge University Press:  01 May 2009

MOHAMED EL-GEBEILY  and
DONAL O'REGAN
MOHAMED EL-GEBEILY
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia e-mail: mgebeily@kfupm.edu.sa
DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland Galway, Ireland e-mail: donal.oregan@nuigalway.ie
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Abstract

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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).

Keywords

34B1534A34
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 385 - 404
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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