Asymptotic Distribution of Eigenvalues for Schrödinger Operators with Magnetic Fields

Asymptotic Distribution of Eigenvalues for Pauli Operators with Nonconstant Magnetic Fields

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

Counting Eigenvalues of Biharmonic Operators with Magnetic Fields

An analysis is given of the spectral properties of perturbations of the magnetic bi-harmonic operator ∆A in L(R), n=2,3,4, where A is a magnetic vector potential of Aharonov-Bohm type, and bounds for the number of negative eigenvalues are established. Key elements of the proofs are newly derived Rellich inequalities for ∆A which are shown to have a bearing on the limiting cases of embedding the...

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Asymptotic Distribution of Eigenvalues for Some Elliptic Operators with Simple Remainder Estimates

We are interested in remainder estimates in the Weyl formula for the asymptotic number of eigenvalues of certain elliptic operators on R and on a smooth compact manifold without boundary. The main aim of this paper is to compare spectral asymptotics of operators with irregular coefficients and certain classes of smoothed operators for which the Weyl formula is derived by means of elementary pse...