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Conditions of spectrum localization for operators not close to self-adjoint operators. (English. Russian original) Zbl 1494.47036

Dokl. Math. 97, No. 2, 170-173 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 479, No. 5, 497-500 (2018).
Summary: The Keldysh theorem is generalized to an arbitrary closed operator that is not necessarily close to self-adjoint operators and has a resolvent of Schatten-von Neumann class \(\mathfrak{S}_p\). Based on this theorem, conditions of spectrum localization are obtained for certain classes of non-self-adjoint differential operators.

MSC:

47B28 Nonselfadjoint operators
47E05 General theory of ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
47A10 Spectrum, resolvent
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References:

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