Geodesic
Molchanov's criterion for compactness of the resolvent for a nonselfadjoint Sturm–Liouville operator
Sbornik. Mathematics, Tome 215 (2024) no. 9, pp. 1249-1268 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Molchanov-type condition is considered in applications to ordinary differential operators of arbitrary order with complex-valued coefficients. It is proved to be a necessary condition for the compactness of the resolvent for a wide class of operators of this type. A counterexample is given showing that this condition does not suffice for the compactness of the resolvent for a Sturm–Liouville operator with nonnegative real part of the potential. Molchanov's criterion is generalized to potentials taking values in a sector bounded away from the negative half-axis and more narrow than a half-plane. Bibliography: 18 titles.
Keywords: nonselfadjoint Sturm–Liouville operator, discreteness of spectrum, compactness of resolvent, Molchanov's criterion. 
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S. N. Tumanov. Molchanov's criterion for compactness of the resolvent for a nonselfadjoint Sturm–Liouville operator. Sbornik. Mathematics, Tome 215 (2024) no. 9, pp. 1249-1268. http://geodesic.mathdoc.fr/item/SM_2024_215_9_a5/

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