Spectral invariance for pseudodifferential operators in Holder-Zygmund spaces of the variable smoothness

摘要

We consider the Holder-Zygmund spaces of the variable smoothness. The smoothness depends on a point in the space and may take negative values. We study the invertibility of pseudodifferential operators with symbols from the Hormander classes of zero order and prove coincidence of the spectra of considered operators in various spaces.