October 13, 2025Open Access

Spectral theory for semigroups on locally convex spaces

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The study reveals new spectral inclusion theorems for semigroups, enhancing understanding in functional analysis.
Key findings show extended results for strongly continuous semigroups, previously confined to Banach spaces.
The research employs a theoretical framework based on locally convex spaces to analyze semigroup behaviour.
These findings expand classical theory, suggesting new avenues for analysis in modern mathematics.

Implication

This paper provides spectral inclusion theorems for continuous semigroups in locally convex spaces, extending known results.

Abstract

In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for strongly continuous semigroups on Banach spaces.

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Cite This Study

Karsten Kruse (2025) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0967b https://doi.org/10.48550/arxiv.2509.11931

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Implication

This paper provides spectral inclusion theorems for continuous semigroups in locally convex spaces, extending known results.

Spectral theory for semigroups on locally convex spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Spectral theory for semigroups on locally convex spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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