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Strong operator convergence and spectral theory of ordinary differential operators. (English) Zbl 0964.47004

The author studies a generalized version of strong resolvent convergence, where the Hilbert spaces on which the operators act may be varying subspaces of a fixed space. This situation occurs when Sturm-Liouville operators are approximated by problems on smaller intervals. Some applications of this type are discussed.

MSC:

47A58 Linear operator approximation theory
34L05 General spectral theory of ordinary differential operators
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