Smoothing of operator semigroups under relatively bounded perturbations

Fuente: arXiv
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Main Authors: Arora, Sahiba, Mui, Jonathan
Format: Preprint
Published: 2025
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_version_ 1866911663359262720
author Arora, Sahiba
Mui, Jonathan
author_facet Arora, Sahiba
Mui, Jonathan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_18556
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Smoothing of operator semigroups under relatively bounded perturbations
Arora, Sahiba
Mui, Jonathan
Analysis of PDEs
Functional Analysis
34G10, 35B20, 35P05, 47A10, 47A55, 47B65, 47D06
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.
title Smoothing of operator semigroups under relatively bounded perturbations
topic Analysis of PDEs
Functional Analysis
34G10, 35B20, 35P05, 47A10, 47A55, 47B65, 47D06
url https://arxiv.org/abs/2501.18556