Local completeness for eigenfunctions of regular maximal ordinary differential operators

Author:
Robert Carlson

Journal:
Proc. Amer. Math. Soc. **79** (1980), 400-404

MSC:
Primary 47E05; Secondary 34B25

DOI:
https://doi.org/10.1090/S0002-9939-1980-0567980-2

MathSciNet review:
567980

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Abstract: Let be a differential operator on with infinitely differentiable matrix valued coefficients. Assume that for . The domain of *L* is the set of *k*-vector valued functions *f* such that is absolutely continuous on [0, 1] and . Let . Then there is a neighborhood containing such that the restrictions of the eigenfunctions of *L* to have dense span in . The example shows that this is the best possible abstract result.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0567980-2

Article copyright:
© Copyright 1980
American Mathematical Society