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Schatten class generalized Toeplitz operators on the Bergman space

Chunxu Xu, Tao Yu (2021)

Czechoslovak Mathematical Journal

Let μ be a finite positive measure on the unit disk and let j 1 be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator T μ ( j ) to be bounded or compact. We first give a necessary and sufficient condition for T μ ( j ) to be in the Schatten p -class for 1 p < on the Bergman space A 2 , and then give a sufficient condition for T μ ( j ) to be in the Schatten p -class ( 0 < p < 1 ) on A 2 . We also discuss the generalized Toeplitz operators with general bounded symbols. If ϕ L ( D , d A ) and 1 < p < , we define the generalized Toeplitz...

Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field

A. Iantchenko, E. Korotyaev (2010)

Mathematical Modelling of Natural Phenomena

We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.

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