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On Molchanov's criterion for compactness of the resolvent for a non self-adjoint Sturm-Liouville operator (2402.10577v1)
Published 16 Feb 2024 in math.SP
Abstract: The Molchanov's condition is a necessary condition for the compactness of the resolvent for a wide class of ordinary differential operators of arbitrary order, but for the Sturm-Liouville operator it is not sufficient, even if the real part of the potential is non-negative. Molchanov's criterion remains valid in the formulation closest to the original one for potentials that take values in a narrower sector than the half-plane, separated from the negative half-axis. This work is devoted to these questions.