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The spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian in the plane with a delta-potential supported on a finite curve are studied. After a general discussion of the qualitative spectral properties of the perturbed Landau Hamiltonian and its resolvent, one of our main objectives is a local spectral analysis near the Landau levels.
This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. Raikov.[-]
The spectral properties of a singularly perturbed self-adjoint Landau Hamiltonian in the plane with a delta-potential supported on a finite curve are studied. After a general discussion of the qualitative spectral properties of the perturbed Landau Hamiltonian and its resolvent, one of our main objectives is a local spectral analysis near the Landau levels.
This talk is based on joint works with P. Exner, M. Holzmann, V. Lotoreichik, and G. ...[+]

47A55 ; 47N50 ; 81Q10

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Clark measures for rational inner functions - Sola, Alan (Author of the conference) | CIRM H

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Reporting on joint work with K. Bickel and J. Cima, I will present a detailed analysis of Clark measures and Clark isometries associated with rational inner functions on the bidisk. I will also indicate some applications to the study of extreme points of the set of positive pluriharmonic measures in two dimensions.

28A25 ; 28A35 ; 47A55

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