Abstract
One proves the absence of positive eigenvalues for the Schrödinger and Stark operators with the use of Hardy-type inequalities.
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Literature cited
A. F. Vakulenko, “Multidimensional Hardy inequalities and the absence of positive eigenvalues for the Schrödinger operator with complex potential,” J. Sov. Math.,32, No. 5 (1986).
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R. Froese, I. Herbst, M. Hoffmann-Ostenhof, and T. Hoffmann-Ostenhof, “On the absence of positive eigenvalues for one-body Schrödinger operators,” J. Analyse Math.,41, 272–284 (1982).
J. E. Avron and I. W. Herbst, “Spectral and scattering theory of Schrödinger operators related to the Stark effect,” Commun. Math. Phys.,52, No. 3, 239–254 (1977).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 13–17, 1985.
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Vakulenko, A.F. Treves inequality and the absence of positive eigenvalues for the Schrödinger operator with a complex potential. J Math Sci 37, 799–802 (1987). https://doi.org/10.1007/BF01387719
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DOI: https://doi.org/10.1007/BF01387719