Asymptotic of complex hyperbolic geometry and L2-spectral analysis of Landau-like Hamiltonians

In this paper we show that the flat Hermitian complex geometry of Cn, n⩾1, is approximated by the complex hyperbolic geometry of the Bergman complex balls Bρn⊂Cn of radius ρ>0. Furthermore, it will be shown that some elements of the L2-spectral analysis, such as the spectrum, the L2-eigenprojecto...

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Bibliographic Details
Published in:Journal of mathematical physics 2005-03, Vol.46 (3), p.032107.1-032107.26
Main Authors: GHANMI, Allal, INTISSAR, Ahmed
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary:In this paper we show that the flat Hermitian complex geometry of Cn, n⩾1, is approximated by the complex hyperbolic geometry of the Bergman complex balls Bρn⊂Cn of radius ρ>0. Furthermore, it will be shown that some elements of the L2-spectral analysis, such as the spectrum, the L2-eigenprojector and the resolvent kernels, associated to the so-called Landau-like Hamiltonian HB,ρ on Bρn give rise to their analogous of the Landau-like Hamiltonian HB,∞ on Cn by letting ρ tend to infinity.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1853505