Proceedings of the American Mathematical Society

Author(s): Giorgio Metafune; Diego Pallara
Journal: Proc. Amer. Math. Soc. 130 (2002), 1779-1786.
MSC (2000): Primary 35J10; Secondary 35P15
Posted: November 9, 2001
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Abstract: We give estimates on the bottom of the essential spectrum of Schrödinger operators $-\Delta+V$ in $L^2(\mathbf{R}^N)$ .

1.: E. B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, 1989. MR 92a:35035
2.: E. B. Davies, Spectral theory and differential operators, Cambridge Univ. Press, 1995. MR 96h:47056
3.: D. E. Edmunds, W. D. Evans, Spectral theory and differential operators, Oxford U.P., 1987. MR 89b:47001
4.: D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Springer, 1983. MR 86c:35035
5.: V. Kondrat'ev, M. Shubin, Discreteness of spectrum for the Schrödinger operators on manifolds with bounded geometry, in Operator theory: advances and applications, 110 (dedicated to V.G.Maz'ya 60th anniversary), Birkhäuser, 1999, 185-226. MR 2001c:58030
6.: V. G. Maz'ya, Sobolev Spaces, Springer, 1985. MR 87g:46056
7.: V. G. Maz'ya, M. Otelbaev, Imbedding theorems and the spectrum of a pseudodifferential operator, Siberian Math. J., 18 (1978), 758-769. MR 56:12873
8.: G. Metafune, D. Pallara, Discreteness of the spectrum for some differential operators with unbounded coefficients in ${\mathbf R}^n$ , Rend. Mat. Acc. Lincei, s.9, 11 (2000), 9-19. CMP 2001:05
9.: A. M. Molcanov, Conditions for the discreteness of the spectrum of self-adjoint second-order differential equations, Trudy Moskov Mat. Obsc. 2 (1953), 169-200 (in Russian). MR 15:224g
10.: B. Simon, Some quantum operators with discrete spectrum but classically continuous spectrum, Annals of Physics, 146 (1983), 209-220. MR 85d:35089
11.: E. M. Stein, Harmonic Analysis, Princeton Univ. Press, 1993. MR 95c:42002
12.: G. Talenti, Best constants in Sobolev inequality, Ann. Mat. Pura Appl., 110 (1976), 353-372. MR 57:3846

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Giorgio Metafune
Affiliation: Dipartimento di Matematica ``Ennio De Giorgi'', Università di Lecce, C.P.193, 73100, Lecce, Italy
Email: metafune@le.infn.it

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