Several authors have considered eigenvalue problems for differential equations where the eigenvalue parameter also appears in the boundary conditions. Such problems do not appear to arise from any spectral problem associated with a linear operator on a Hilbert space. However, it is possible to reset such problems in this context. This has been done for certain second order cases by Walter [4] using a special measure on the interval in question, and by Fulton [1, 2] using the type of space indicated in the title of this article.It is our purpose here to consider a general class of operators on L 2(I) ⊕ Cr , which are based on a differential expression τ of order n on I. We shall first investigate adjoints, boundary conditions, and self-adjointness for such operators. We shall then show that all eigenvalue problems of the form τy = λy, with boundary conditions which involve λ in a linear fashion, can be reset in the context of such operators.
@article{10_4153_CJM_1987_003_1,
author = {Kemp, R. R. D.},
title = {Operators on {L} {2(I)} \ensuremath{\oplus} {Cr}},
journal = {Canadian journal of mathematics},
pages = {33--53},
year = {1987},
volume = {39},
number = {1},
doi = {10.4153/CJM-1987-003-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-003-1/}
}
TY - JOUR
AU - Kemp, R. R. D.
TI - Operators on L 2(I) ⊕ Cr
JO - Canadian journal of mathematics
PY - 1987
SP - 33
EP - 53
VL - 39
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-003-1/
DO - 10.4153/CJM-1987-003-1
ID - 10_4153_CJM_1987_003_1
ER -
%0 Journal Article
%A Kemp, R. R. D.
%T Operators on L 2(I) ⊕ Cr
%J Canadian journal of mathematics
%D 1987
%P 33-53
%V 39
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-003-1/
%R 10.4153/CJM-1987-003-1
%F 10_4153_CJM_1987_003_1
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Walter, J., Regular eigenvalue problems with eigenvalue parameter in the boundary conditions, Math. Z.133(1973), 301–312. Google Scholar
