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arXiv · 2003.00966

Invariance of the Fredholm Index and Spectrum of Non-Smooth Pseudodifferential Operators

Helmut Abels·Christine Pfeuffer
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Abstract

In this paper we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in H\"older spaces. By means of this invariance we improve previous spectral invariance results for non-smooth pseudodifferential operators $P$ with coefficients in H\"older spaces. For this purpose we approximate $P$ with smooth pseudodifferential operators and use a spectral invariance result of smooth pseudodifferential operators. Then we get the spectral invariance result in analogy to a proof of the spectral invariance result for non-smooth differential operators by Rabier.

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Helmut Abels, Christine Pfeuffer. 2020-03-02. Invariance of the Fredholm Index and Spectrum of Non-Smooth Pseudodifferential Operators. https://arxiv.org/abs/2003.00966

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