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

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 , X = { f ∈ C ( n - 1 ) [ 0 , 1 ] : f ( n ) ∈ X } where X is an interpolation space between L 1 [ 0 , 1 ] and L ∞ [ 0 , 1 ] .