Absolute continuity of eigenvectors of time-varying operators
Andrew F. Acker
Proc. Amer. Math. Soc. 42 (1974), 198-201
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Abstract: If 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 is a commuting set provided that commutes with its time derivative at each t. The distinct eigenvalue condition is shown to be necessary.
A. Acker, Stability results for linear systems involving a time varying unbounded operator, Doctoral Dissertation, Boston University, 1972, Appendix B.
- A. Acker, Stability results for linear systems involving a time varying unbounded operator, Doctoral Dissertation, Boston University, 1972, Appendix B.
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Compact operator function,
eigenvalue and eigenvector functions,
"real'' Hilbert space,
commuting set of operators
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