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

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.

References in corpus (1)

• Approximating L2-invariants, and the Atiyah conjecture

Cited by in corpus (3)

• Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence
• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb{Z}}^d$