Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
MathSciNet review: 567980
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ L = \sum\nolimits_{m = 0}^n {{A_m}(x){D^m}} $ be a differential operator on $ { \oplus ^k}{L^2}[0,1]$ with infinitely differentiable $ k \times k$ matrix valued coefficients. Assume that $ \det \,{A_n}(x) \ne 0$ for $ x \in [0,1]$. The domain of L is the set of k-vector valued functions f such that $ f \in {C^{n - 1}}([0,1]),{f^{(n - 1)}}$ is absolutely continuous on [0, 1] and $ Lf \in { \oplus ^k}{L^2}[0,1]$. Let $ {x_0} \in (0,1)$. Then there is a neighborhood $ U({x_0})$ containing $ {x_0}$ such that the restrictions of the eigenfunctions of L to $ U({x_0})$ have dense span in $ { \oplus ^k}{L^2}[U({x_0})]$. The example $ L = {e^{ - ix}}d/dx$ shows that this is the best possible abstract result.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47E05, 34B25

Retrieve articles in all journals with MSC: 47E05, 34B25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0567980-2
PII: S 0002-9939(1980)0567980-2
Article copyright: © Copyright 1980 American Mathematical Society