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arXiv · 2012.11092

Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces

Tiffany Frugé Jones·Joshua Lee Padgett·Qin Sheng
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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.

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Tiffany Frugé Jones, Joshua Lee Padgett, Qin Sheng. 2020-12-21. Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces. https://arxiv.org/abs/2012.11092

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