Absolute continuity of eigenvectors of time-varying operators
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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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