zbMATH — the first resource for mathematics

On the absence of positive eigenvalues for one-body Schrödinger operators. (English) Zbl 0512.35062

35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35B60 Continuation and prolongation of solutions to PDEs
Full Text: DOI
[1] S. Agmon,Lower bounds for solutions of Schrödinger equations, J. Analyse Math.23 (1970), 1–25. · Zbl 0211.40703 · doi:10.1007/BF02795485
[2] W. O. Amrein, A. M. Berthier and V. Georgescu,L p -inequalities for the Laplacian and unique continuation, Ann. Inst. Fourier, Grenoble31 (3) (1981), 153–168. · Zbl 0468.35017
[3] M. S. P. Eastham and H. Kalf,Schrödinger operators with continuous spectrum, Pitman Research Notes Series, London, to appear. · Zbl 0491.35003
[4] R. Froese, I. Herbst, M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof,L 2-exponential lower bounds to solutions of the Schrödinger equation, to appear in Commun. Math. Phys.
[5] V. Georgescu,On the unique continuation property for Schrödinger Hamiltonians, Helv. Phys. Acta52 (1979), 655–670.
[6] L. Hörmander,Théorie de la diffusion à courte portée pour des opérateurs à caractéristiques simples, preprint, 1981.
[7] L. Hörmander, personal communication.
[8] T. Kato,Growth properties of solutions of the reduced wave equation with variable coefficients, Comm. Pure Appl. Math.12 (1959), 403–425. · Zbl 0091.09502 · doi:10.1002/cpa.3160120302
[9] R. Lavine,Constructive estimates in quantum scattering, unpublished manuscript. · Zbl 0999.81084
[10] H. A. Levine,On the positive spectrum of Schrödinger operators with long range potentials, inSpectral Theory of Differential Operators, I. W. Knowles and R. T. Lewis (eds.), North-Holland Mathematics Studies, Amsterdam, North-Holland, 1981. · Zbl 0495.34013
[11] B. Simon,On the positive eigenvalues of one-body Schrödinger operators, Comm. Appl. Math.22 (1969), 531–538. · Zbl 0167.11003
[12] B. Simon,Trace Ideals and Their Applications, Cambridge University Press, Cambridge, 1979. · Zbl 0423.47001
[13] J. von Neumann and E. P. Wigner,Über merkwürdige diskrete Eigenwerte, Z. Phys.30 (1929), 465–467. · JFM 55.0520.04
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.