Mathematical Methods in the Applied Sciences· 2026Q2
Generalized Semigroups and Moderate Resolvent Conditions
- 0citations
- Q2SCImago
- 2026year
Short summary
Researchers developed a generalized Hille-Yosida and perturbation framework for $\mathcal{A}$-semigroups in Colombeau-type operator algebras, establishing generation and stability under perturbations from operator nets satisfying moderate resolvent bounds.
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Key points
- Developed a generalized Hille-Yosida and perturbation framework for $\mathcal{A}$-semigroups in Colombeau-type operator algebras.
- Established generation and stability under bounded and negligible perturbations for operator nets satisfying moderate resolvent bounds.
- Derived resolvent estimates from dissipativity.
- Extended classical semigroup methods to parameter-dependent families with singular asymptotic behavior.
- Applied the framework to regularized Schrödinger operators and the heat equation with singular potential, recovering the Feynman-Kac semigroup.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT We develop a generalized Hille–Yosida and perturbation framework for ‐semigroups in Colombeau‐type operator algebras. Starting from operator nets satisfying moderate resolvent bounds, we establish generation, stability under bounded and negligible perturbations, and resolvent estimates derived from dissipativity This extends classical semigroup methods to parameter‐dependent families with singular asymptotic behavior. Applications are given to regularized Schrödinger operators and to the heat equation with singular potential, recovering the Feynman–Kac semigroup in the generalized setting.
The authors' abstract, as published at the source. Mathematical Methods in the Applied Sciences, 2026 · DOI ↗
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