Counting Eigenvalues of Biharmonic Operators with Magnetic Fields
نویسندگان
چکیده
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 theorems for Sobolev spaces H(R).
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Semi-classical Asymptotics for the Counting Functions and Riesz Means of Pauli and Dirac Operators with Large Magnetic Fields
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