Absolute continuity of eigenvectors of time-varying operators
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- by Andrew F. Acker PDF
- Proc. Amer. Math. Soc. 42 (1974), 198-201 Request permission
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
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A. Acker, Stability results for linear systems involving a time varying unbounded operator, Doctoral Dissertation, Boston University, 1972, Appendix B.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 198-201
- MSC: Primary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326457-7
- MathSciNet review: 0326457