Eigenvalue distribution of canonical systems: trace class and sparse spectrum

2024/12/28 by Matthias Langer, Langer, Matthias, Jakob Reiffenstein +3
Mathematics · #advanced mathematical theories #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2412.20124

Abstract

In this paper we consider two-dimensional canonical systems with discrete spectrum and study their eigenvalue densities. We develop a formula that determines the Stieltjes transform of the eigenvalue counting function up to universal multiplicative constants. An explicit criterion is given for the resolvents of the model operator to belong to a Schatten-von Neumann class with index 0

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