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arXiv · 2607.29354

Localisation of pseudospectra on discrete groups

Simon N. Chandler-Wilde·Marko Lindner·Christian Seifert
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Abstract

In this paper we generalise two of the methods and corresponding results from our previous paper ``On spectral inclusion sets and computing the spectra and pseudospectra of bounded linear operators'' [J. Spectr. Theory 14 (2024), 719--804] from tridiagonal operators on $\ell^2(\Z)$ to band operators $A$ on $\ell^2(G,Y)$ with a countable Abelian group $G$ and a Hilbert space $Y$. Again, we cover the pseudospectra of $A$, with error-control, via a union of pseudospectra of finite and moderately sized ``local patches'' of $A$. While a major application is to understand the case $G=\Z^d$ that is immanent in many physical problems, our new approach to the so-called $τ$ and $τ_1$ methods immediately extends to countable Abelian groups $G$.

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Simon N. Chandler-Wilde, Marko Lindner, Christian Seifert. 2026-07-31. Localisation of pseudospectra on discrete groups. https://arxiv.org/abs/2607.29354

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