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arXiv · 1811.09892

Asymptotics of determinants for finite sections of operators with almost periodic diagonals

Torsten Ehrhardt·Zheng Zhou
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Abstract

Let $A = (a_{j,k})_{j,k=-\infty}^\infty$ be a bounded linear operator on $l^2(\mathbb{Z})$ whose diagonals $D_n(A) = (a_{j,j-n})_{j=-\infty}^\infty\in l^\infty(\mathbb{Z})$ are almost periodic sequences. For certain classes of such operators and under certain conditions, we are going to determine the asymptotics of the determinants $\det A_{n_1,n_2}$ of the finite sections of the operator $A$ as their size $n_2 - n_1$ tends to infinity. Examples of such operators include block Toeplitz operators and the almost Mathieu operator.

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Torsten Ehrhardt, Zheng Zhou. 2018-11-24. Asymptotics of determinants for finite sections of operators with almost periodic diagonals. https://arxiv.org/abs/1811.09892

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