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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Differential-boundary operators


Author: Allan M. Krall
Journal: Trans. Amer. Math. Soc. 154 (1971), 429-458
MSC: Primary 34.30
DOI: https://doi.org/10.1090/S0002-9947-1971-0271445-4
Addendum: Trans. Amer. Math. Soc. 180 (1973), 505.
MathSciNet review: 0271445
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Abstract: Differential-boundary systems occur naturally as adjoints for ordinary differential systems involving integral boundary conditions. In this paper such systems are generalized so that the adjoint system has the same form as the original. Interior boundary points are introduced and removed, and the integrals, used in the boundary conditions, are also removed. Selfadjoint systems are classified, and an eigenfunction expansion is derived. Finally, nonselfadjoint systems are discussed and again, an eigenfunction expansion is derived.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0271445-4
Keywords: Operator, differential operator, boundary value problem, differential system, selfadjoint, nonselfadjoint, Sturm-Liouville problem, adjoint, eigenvalue, spectrum, spectral resolution
Article copyright: © Copyright 1971 American Mathematical Society