Scattering Length and the Spectrum of –Δ + V
Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 144-151

Voir la notice de l'article provenant de la source Cambridge University Press

Given a non-negative, locally integrable function $V$ on ${{\mathbb{R}}^{n}}$ , we give a necessary and sufficient condition that $-\Delta +V$ have purely discrete spectrum, in terms of the scattering length of $V$ restricted to boxes.
DOI : 10.4153/CMB-2006-015-5
Mots-clés : 35J10
Taylor, Michael. Scattering Length and the Spectrum of –Δ + V. Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 144-151. doi: 10.4153/CMB-2006-015-5
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[F] Friedrichs, K., Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren. Math. Ann. 109(1934), 465–487, 685–713. Google Scholar

[K] Kac, M., Probabilistic methods in some problems of scattering theory. Rocky Mountain J. Math. 4(1974), 511–537. Google Scholar

[KL] Kac, M. and Luttinger, J., Scattering length and capacity. Ann. Inst. Fourier 25(1975), no. 3–4, 317–321. Google Scholar

[KS] Kondrat’ev, V. and Shubin, M., Discreteness of spectrum for the Schrødinger operators on manifolds with bounded gaometry. Oper. Theory Adv. Appl. 110, Birkhauser, Basel, 1999, pp. 185–226. Google Scholar

[MS] Maz’ya, V. and Shubin, M., Discreteness of spectrum and positivity criteria for Schrödinger operators. Ann. Math. 162(2005), 919–942. Google Scholar

[Mol] Molchanov, A., On conditions for the discreteness of the spectrum conditions for self-adjoint differential equations of the second order. Proc. Moscow Math. Soc. 2(1953), 169–199. (Russian) Google Scholar

[T] Taylor, M., Scattering length and perturbations of Δ by positive potentials. J. Math. Anal. Appl. 53(1976), no. 2, 291–312. Google Scholar

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