On the Essential Spectrum of Two-Dimensional Pauli Operators with Repulsive Potentials

Institute for Mathematical Physics on the Essential Spectrum of Two Dimensional Periodic Magnetic Schrr Odinger Operators on the Essential Spectrum of Two Dimensional Periodic Magnetic Schrr Odinger Operators

For two dimensional Schrr odinger operators with a nonzero constant magnetic eld perturbed by an innnite number of periodically disposed, long range magnetic and electric wells, it is proven that when the inter-well distance (R) grows to innnity, the essential spectrum near the eigenvalues of the \one well Hamiltonian" is located in mini-bands whose width shrink faster than any exponential with...

Spectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

Measure of non strict singularity of Schechter essential spectrum of two bounded operators and application

In this paper‎, ‎we discuss the essential spectrum of sum of two bounded operators‎ ‎using measure of non strict singularity‎. ‎Based on this new investigation‎, ‎a problem of one-speed neutron transport operator is presented‎.

On the Absolutely Continuous Spectrum of Multi-dimensional Schrödinger Operators with Slowly Decaying Potentials

1. In this short paper we extend the method of Laptev-Naboko-Safronov [15]. New estimates for the discrete spectrum obtained in this paper allow one to prove stronger results compared to [15]. The main technical tool of the paper [15] is the so called trace inequality, which relates properties of negative eigenvalues to the properties of the a.c. spectrum. Based on this relation, the technique ...

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields