Pseudospectral phenomena preventing the analyticity sector of a Ornstein-Uhlenbeck semigroup to be ruled by the spectral angle of its generator

Karel Pravda-Starov

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arXiv · 2610.33683

Pseudospectral phenomena preventing the analyticity sector of a Ornstein-Uhlenbeck semigroup to be ruled by the spectral angle of its generator

Karel Pravda-Starov

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Abstract

We study elliptic Ornstein-Uhlenbeck operators in $L^2$ spaces with respect to invariant measures. These operators have discrete spectra and generate analytic semigroups. The angle defining the analyticity sector of a Ornstein-Uhlenbeck semigroup is not always equal to the complementary angle of the spectral angle of its generator. In this work, we study the link between these two angles. More specifically, we provide a necessary and sufficient criterion ensuring that they are complementary, and explain how pseudospectral phenomena account for these two angles to fail to be complementary.

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Karel Pravda-Starov. 2026-10-24. Pseudospectral phenomena preventing the analyticity sector of a Ornstein-Uhlenbeck semigroup to be ruled by the spectral angle of its generator. https://arxiv.org/abs/2610.33683

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