$L^p$-approximation of the integrated density of states for Schrödinger operators with finite local complexity

Details $L^p$-approximation of the integrated density of states for Schrödinger operators with finite local complexity $L^p$-approximation of the integrated density of states for Schrödinger operators with finite local complexity

2010-04-20

arxiv.org/abs/1004.3471v2

Integral Equations Operator Theory 69.2 (2011), 217-232

Mathematics

Spectral Theory

15 pages; v2 has minor fixes

Scientific paper

10.1007/s00020-010-1831-6

We study spectral properties of Schr\"odinger operators on $\RR^d$. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in $\ZZ^d$, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.

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