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

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

2006-07-07

arxiv.org/abs/math/0607198v1

Mathematics

Functional Analysis

Scientific paper

Introducing and studying the pattern frequency algebra, we prove the analogue
of L\"uck'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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