Quantitative inductive estimates for Green’s functions of non-self-adjoint matrices

Liu, Wencai

doi:10.2140/apde.2022.15.2061

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Quantitative inductive estimates for Green's functions of non-self-adjoint matrices

Wencai Liu

Vol. 15 (2022), No. 8, 2061–2108

DOI: 10.2140/apde.2022.15.2061

Abstract

We provide quantitative inductive estimates for Green’s functions of matrices with (sub-)exponentially decaying off-diagonal entries in arbitrary dimensions. Together with Cartan’s estimates and discrepancy estimates, we establish explicit bounds for the large-deviation theorem for non-self-adjoint Toeplitz operators. As applications, we obtain the modulus of continuity of the integrated density of states with explicit bounds and the pure point spectrum property for analytic quasiperiodic operators. Moreover, our inductions are self-improved and work for perturbations with low-complexity interactions.

Keywords

multiscale analysis, large-deviation theorem, discrepancy, semialgebraic sets, Cartan's techniques, Anderson localization

Mathematical Subject Classification

Primary: 81Q10

Secondary: 37C55, 82B44

Milestones

Received: 24 September 2020

Revised: 29 March 2021

Accepted: 19 May 2021

Published: 10 February 2023

Authors

Wencai Liu
Department of Mathematics Texas A&M University College Station, TX United States

Vol. 15, No. 8, 2022