Spectral Invariance of Non-Smooth Pseudodifferential Operators
Abstract
In this paper we discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in H\"older spaces. In analogy to the proof in the smooth case of Beals and Ueberberg, we use the characterization of non-smooth pseudodifferential operators to get such a result. The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols and the fact, that in general the composition of two non-smooth pseudodifferential operators is not a pseudodifferential operator. In order to improve these spectral invariance results for certain subsets of non-smooth pseudodifferential operators with coefficients in H\"older spaces, we improve the characterization of non-smooth pseudodifferential operators in a previous work by the authors.
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Cite
@article{arxiv.1512.08795,
title = {Spectral Invariance of Non-Smooth Pseudodifferential Operators},
author = {Helmut Abels and Christine Pfeuffer},
journal= {arXiv preprint arXiv:1512.08795},
year = {2016}
}
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43 pages