On the spectrum of Bargmann-Toeplitz operators with symbols of a variable sign

Details On the spectrum of Bargmann-Toeplitz operators with symbols of a variable sign On the spectrum of Bargmann-Toeplitz operators with symbols of a variable sign

2009-12-22

arxiv.org/abs/0912.4486v1

Mathematics

Spectral Theory

19 pages, Latex

Scientific paper

The paper discusses the spectrum of Toeplitz operators in Bargmann spaces. Our Toeplitz operators have real symbols with a variable sign and a compact support. A class of examples is considered where the asymptotics of the eigenvalues of such operators can be computed. These examples show that this asymptotics depends on the geometry of the supports of the positive and negative parts of the symbol. Applications to the perturbed Landau Hamiltonian are given.

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