Journal of Mathematics of Kyoto University
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J. Math. Kyoto Univ. 48 (2008), no. 3,  p. 597 - 616
Magnetic bottles on the Poincaré half-plane: spectral asymptotics
Abderemane Morame and Françoise Trcu

We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$\\ on the Poincar\'e upper-half plane $\bH \; ,$ when the magnetic field $dA$ is infinite at the infinity such that $-\Delta_A$ has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.

2000 Mathematics Subject Classification
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©2008 Department of Mathematics, Kyoto University