Abstract:
The spectral properties of the Sturm–Liouville operator on the semi-axis with the complex-valued potential with the range exceeding the half-plane, has been little studied. The operator in this case can be non-sectorial, the numerical range can coincide with the entire complex plane. In this situation we propose the conditions ensuring the discreteness of the spectrum and the compactness of the resolvent.
Citation:
S. N. Tumanov, “On one condition for the discreteness of the spectrum and the compactness of the resolvent of a nonsectorial Sturm–Liouville operator on the semiaxis”, Dokl. RAN. Math. Inf. Proc. Upr., 510 (2023), 39–42; Dokl. Math., 107:2 (2023), 117–119
\Bibitem{Tum23}
\by S.~N.~Tumanov
\paper On one condition for the discreteness of the spectrum and the compactness of the resolvent of a nonsectorial Sturm--Liouville operator on the semiaxis
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 510
\pages 39--42
\mathnet{http://mi.mathnet.ru/danma378}
\crossref{https://doi.org/10.31857/S2686954323700145}
\elib{https://elibrary.ru/item.asp?id=53986710}
\transl
\jour Dokl. Math.
\yr 2023
\vol 107
\issue 2
\pages 117--119
\crossref{https://doi.org/10.1134/S1064562423700734}
Linking options:
https://www.mathnet.ru/eng/danma378
https://www.mathnet.ru/eng/danma/v510/p39
This publication is cited in the following 2 articles:
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