We derive some bounds on the location of complex eigenvalues for a family of Schrödinger operators defined on the positive half line and subject to integrable complex potential. We generalise the results obtained in  where the operator does not have a Hardy term and also include the analysis for potentials belonging to weighted spaces. Some information on the geometry of the complex region which bounds the eigenvalues of the radial Schrödinger multidimensional operator are then recovered.
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Francesco Ferrulli, Ari Laptev, Complex eigenvalue bounds for a Schrödinger operator on the half line. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 1–13DOI 10.4171/RLM/876