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arXiv · 2501.18556

Smoothing of operator semigroups under relatively bounded perturbations

Sahiba Arora·Jonathan Mui
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Abstract

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded perturbations of the semigroup generator. This result yields a spectral perturbation theorem, which has implications for the long-term dynamics of evolution equations driven by elliptic operators of second and higher orders. In particular, a new perturbation theorem for so-called eventually positive semigroups is derived as a consequence of the general results.

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Sahiba Arora, Jonathan Mui. 2025-01-30. Smoothing of operator semigroups under relatively bounded perturbations. https://doi.org/10.1016/j.jmaa.2026.130640

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