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Proceedings of the American Mathematical Society

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Absolute continuity of eigenvectors of time-varying operators

Author: Andrew F. Acker
Journal: Proc. Amer. Math. Soc. 42 (1974), 198-201
MSC: Primary 47B05
MathSciNet review: 0326457
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Abstract: If $ K(t)$ is a compact, selfadjoint operator function of a real variable t with distinct eigenvalues at each t, we show that the eigenvalues and eigenvectors are absolutely continuous and that $ \{ K(t)\} $ is a commuting set provided that $ K(t)$ commutes with its time derivative $ K'(t)$ at each t. The distinct eigenvalue condition is shown to be necessary.

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

  • [1] A. Acker, Stability results for linear systems involving a time varying unbounded operator, Doctoral Dissertation, Boston University, 1972, Appendix B.

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Keywords: Compact operator function, eigenvalue and eigenvector functions, "real'' Hilbert space, selfadjoint, distinct eigenvalues, absolute continuity, commuting set of operators
Article copyright: © Copyright 1974 American Mathematical Society

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