Spectrum of weighted composition operators part IV spectrum and essential spectra of weighted composition operators in spaces of smooth functions on [0,1]

摘要

We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in spaces C-(n)[0, 1] and Sobolev spaces W-n,W- X = {f is an element of C(n- 1)[0, 1] : f ((n)) is an element of X} where X is an interpolation space between L-1 [0, 1] and L-infinity[0, 1].