Zusammenfassung
In this paper, we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in Holder spaces. By means of this invariance, we improve previous spectral invariance results for non-smooth pseudodifferential operators P with coefficients in Holder spaces. For this purpose, we approximate P with smooth pseudodifferential operators and use a spectral ...
Zusammenfassung
In this paper, we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in Holder spaces. By means of this invariance, we improve previous spectral invariance results for non-smooth pseudodifferential operators P with coefficients in Holder 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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