One Condition for Discreteness of the Spectrum and Compactness of the Resolvent of a Nonsectorial Sturm–Liouville Operator on a Semiaxis

The spectral properties of the Sturm–Liouville operator on a semiaxis in the case of a complex-valued potential with a range exceeding the half-plane have been poorly studied. The operator in this case can be nonsectorial: its numerical range can coincide with the entire complex plane. In this situa...

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Bibliographic Details
Published in:Doklady. Mathematics 2023-04, Vol.107 (2), p.117-119
Main Author: Tumanov, S. N.
Format: Article
Language:English
Subjects:
Half planes
Mathematics
Mathematics and Statistics
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Summary:The spectral properties of the Sturm–Liouville operator on a semiaxis in the case of a complex-valued potential with a range exceeding the half-plane have been poorly studied. The operator in this case can be nonsectorial: its numerical range can coincide with the entire complex plane. In this situation, conditions are proposed ensuring the discreteness of the spectrum and the compactness of the resolvent.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562423700734