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Capacity in abstract Hilbert spaces and applications to higher order differential operators. (English) Zbl 0929.47023
Summary: This paper introduces the notion of capacity in abstract Hilbert spaces. It is proved that the spectral shift of a selfadjoint operator which is subjected to a domain perturbation can be estimated in terms of this capacity. The results are finally applied to higher-order partial differential operators.

MSC:
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
47B25 Linear symmetric and selfadjoint operators (unbounded)
46C99 Inner product spaces and their generalizations, Hilbert spaces
47A55 Perturbation theory of linear operators
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