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Boundary conditions for general ordinary differential operators and their adjoints

Published online by Cambridge University Press:  14 November 2011

W. D. Evans  and
Sobhy E. Ibrahim
W. D. Evans
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Senghenydd Road, Cardiff CF2 4AG, Wales, U.K.
Sobhy E. Ibrahim
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Senghenydd Road, Cardiff CF2 4AG, Wales, U.K.
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Synopsis

A characterisation is obtained of all the regularly solvable operators and their adjoints generated by a general differential expression in . The domains of these operators are described in terms of boundary conditions involving the solutions of Mu = λwu and the adjoint equation . The results include those of Sun Jiong [15] concerning self-adjoint realisations of a symmetric M when the minimal operator has equal deficiency indices: if the deficiency indices are unequal the maximal symmetric operators are determined by the results herein. Another special case concerns the J -self-adjoint operators, where J denotes complex conjugation, and for this we recover the results of Zai-jiu Shang in [16].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 99 - 117
Copyright
Copyright © Royal Society of Edinburgh 1990

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