2015/12/29 by Abels, Helmut, Pfeuffer, Christine
#35S05 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1512.08795
In this paper we discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in Hölder 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 Hölder spaces, we improve the characterization of non-smooth pseudodifferential operators in a previous work by the authors.