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$L^2$-spectral invariants and quasi-crystal graphs

Gábor Elek
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Abstract

Introducing and studying the pattern frequency algebra, we prove the analogue of Lück's approximation theorems on $L^2$-spectral invariants in the case of aperiodic order. These results imply a uniform convergence theorem for the integrated density of states as well as the positivity of the logarithmic determinant of certain discrete Schrodinger operators.

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Gábor Elek. 2006-07-07. $L^2$-spectral invariants and quasi-crystal graphs. https://arxiv.org/abs/math/0607198

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