We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.

For a wide class of 2D periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.

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