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Finite Dimensional Perturbations of Differential Expressions

Published online by Cambridge University Press:  20 November 2018

R. R. D. Kemp  and
S. J. Lee
R. R. D. Kemp
Affiliation:
Queen's University, Kingston, Ontario
S. J. Lee
Affiliation:
Queen's University, Kingston, Ontario
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Operators in L2, or more generally, Lp spaces, which are generated by differential expressions, have had extensive study. More recently some authors, in particular Krall [3; 4; 5; 6; 7], Kim [2], and Krall and Brown [8], have studied operators which are generated by a differential expression plus an additional term. This additional term is of the nature of a perturbation of the differential expression by an operator with finite dimensional range. However even if the basic operator is specifically of the form of a finite dimensional perturbation of a differential operator, this is not true of the adjoint, since the boundary conditions which arise on the adjoint are not appropriate to the adjoint of the differential operator alone.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1082 - 1104
Copyright
Copyright © Canadian Mathematical Society 1976

References

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