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- W2000357730 abstract "A perturbation theorem is proved which enables us to extend the results of J. Schwartz and others, to the effect that a wide class of boundary value problems for ordinary differential operators with operator valued coefficients generate unbounded spectral operators in the L 2 space over a finite interval. Thus under mild restrictions on the boundary conditions allowed, an operator ( 1 i d dx ) n + C n−1 ( d dy ) n−1 + B n−2 ( d dx ) n−2 + ··· + B 0 in L 2 [0, 1], where B 0 , …, B n −2 are arbitrary bounded operators and C n −1 is any compact operator plus a bounded one with small norm, is shown to have a complete set of generalized eigenfunctions ( φ n ). Moreover, the series expansions in the φ n are unconditionally convergent." @default.
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- W2000357730 date "1966-03-01" @default.
- W2000357730 modified "2023-09-30" @default.
- W2000357730 title "Perturbation of ordinary differential operators" @default.
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- W2000357730 doi "https://doi.org/10.1016/0022-247x(66)90041-2" @default.
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