Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-29T13:00:46.596Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Kemp, R. R. D., On a class of singular differential operators, Can. J. Math. 13(1961), 316 330.Google Scholar
2. Kim, T. B., The adjoint of a differential-boundary operator with an integral boundary condition on a semiaxis, J. Math. Anal. Appl. 44(1973), 434 446.Google Scholar
3. Krall, A. M., Stieltjes differential-boundary operators II, Pacific J. Math. 55(1974), 207 218.Google Scholar
4. Krall, A. M., Differential-boundary operators, Trans. Amer. Math. Soc. 154(1971), 429 458.Google Scholar
5. Krall, A. M. and Brown, R. C., An eigenfunction expansion for a non-self-adjoint, interior point boundary value problem, Trans. Amer. Math. Soc. 170(1972), 137 147.Google Scholar
6. Krall, A. M., Adjoints of multipoint-integral boundary value problems, Proc. Amer. Math. Soc. 37(1973), 213 216.Google Scholar
7. Krall, A. M., Stieltjes differential-boundary operators, Proc. Amer. Math. Soc. 41(1973), 80 86.Google Scholar
8. Krall, A. M. and Brown, R. C., Ordinary differential operators under stieltjes boundary conditions, Trans. Amer. Math. Soc. 198(1974), 73 92.Google Scholar
9. Rota, G. C., Extension theory of differential operators I, Comm. Pure and Appl. Math. 11(1958), 23 65.Google Scholar