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MAXIMAL ACCRETIVE REALIZATIONS OF REGULAR STURM–LIOUVILLE DIFFERENTIAL OPERATORS

Published online by Cambridge University Press:  24 March 2003

ZONGBEN XU
Affiliation:
Research Center for Applied Mathematics and Institute for Information and System Science, Xi’an Jiaotong University, Xi’an 710049, China
GUANGSHENG WEI
Affiliation:
Research Center for Applied Mathematics and Institute for Information and System Science, Xi’an Jiaotong University, Xi’an 710049, China
PAOLO FERGOLA
Affiliation:
Department of Mathematics, University of Napoli Federico II, Napoli, Italy
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Abstract

Maximal accretive realizations and bound-preserving self-adjoint extensions are two fundamental problems in applications of semi-bounded operator theory to differential equations. On the basis of using differential operator theory in direct sum spaces and Phillips theory for maximal accretive extensions of accretive operators, a complete characterization of the set of maximal accretive boundary conditions for Sturm–Liouville differential operators is presented. As an application, all possible forms of bound-preserving self-adjoint extensions of regular Sturm–Liouville operators are also characterized via various explicit boundary conditions. The methodology can also be applied to dealing with general classes of semi-bounded symmetric differential operators.

Type
Notes and Papers
Copyright
The London Mathematical Society, 2002

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Footnotes

This research is supported by the National Natural Science Foundation of China (10071048).