Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces

TL;DR

This paper extends norm estimates to strongly continuous fractional semigroups in normed vector spaces, addressing a gap in the analysis of solution operators for singular integral equations with applications in modeling non-local phenomena.

Contribution

It introduces the first norm estimates for fractional semigroups solving integral equations in arbitrary normed spaces, generalizing classical semigroup results.

Findings

Established norm estimates for fractional semigroups in normed spaces

Unified classical semigroup results as a special case

Provided a framework for analyzing solution operators of integral equations

Abstract

Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations have recently garnered a large amount of interest due to their potential to model numerous physically relevant phenomena with increased accuracy by incorporating so-called non-local effects. In this article, we provide the first step in the direction of providing such estimates for a particular class of operators which serve as solutions to certain integral equations. The provided results hold in arbitrary normed vector spaces and include the classical results for strongly continuous semigroups as a special case.