L²-spectral invariants and quasi-crystal graphs

2006/07/07 by Gábor Elek, Elek, Gábor
Materials Science · Mathematics · Computer Science · #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.math/0607198

Abstract

Introducing and studying the pattern frequency algebra, we prove the analogue of Lück's approximation theorems on L²-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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