Continuous maximal regularity in locally convex spaces

2024/08/21 by Karsten Kruse, Kruse, Karsten, Felix L. Schwenninger +1 · 1 citation
Mathematics · #46A30 #46A70 #47D06 Secondary 35K90 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Primary 34A12

paper · pdf · doi:10.48550/arxiv.2408.11437

openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly continuous semigroups on Banach spaces. In particular, we show that Travis' characterization of C-maximal regularity using the notion of bounded semivariation carries over to the general case. Under some topological assumptions, we further show the equivalence between maximal regularity and admissibility in this context.

Cited by

• Spectral theory for semigroups on locally convex spaces

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