Bernhard Pfirsch

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20162021

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math.SP2018

A Szegő limit theorem for translation-invariant operators on polygons

Bernhard Pfirsch

We prove Szegő-type trace asymptotics for translation-invariant operators on polygons. More precisely, consider a Fourier multiplier $A = F^{*} σ F$ on $\mathsf{L…

math.SP2016

Formulas of Szegő type for the periodic Schrödinger operator

Bernhard Pfirsch, Alexander V. Sobolev

We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator $H = - \frac{d ^{2}}{d x ^{2}} + V$ in dimension one. Admitting fairly general functions $h$ with $h (0) = 0$ , we…