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Boundary conditions and reducibility of differential operators

Published online by Cambridge University Press:  24 October 2008

B. Fisherl  and
Z. Zahreddine
B. Fisherl
Affiliation:
Westfield College, University of London
Z. Zahreddine
Affiliation:
Westfield College, University of London
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Abstract

Examples were exhibited in [4] of both reducible and irreducible symmetric operators (of deficiency index (1:1)) associated with − d2/dt2 in the Hilbert space L2(I) (I = [0,1). Such symmetric operators are determined by three linearly independent boundary conditions which define their domains as restrictions of the domain of the maximal operator associated with — d2/dt2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 549 - 553
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Coddington, E. A. and Levinson, N.. Theory of Ordinary Differential Equations (McGraw-Hill, 1955).Google Scholar
[2]Denkel, N.. Ph.D. Thesis, University of London, 1980.Google Scholar
[3]Dunford, N. and Schwartz, J. T.. Linear Operators, vol. n (Interscienee, 1963).Google Scholar
[4]FISHEL, B. and Denkel, N.. Reducibility of differential operators: some examples. Math. Proc. Cambridge Philos. Soc. 86 (1979), 29–33.CrossRefGoogle Scholar