Spectrum of Positive Linear Operators and Localization with Regularity of Inverse of Sobolev Deformations

Abstract

Dealing with a characterization of non-negative matrix operators, the spectral localization properties of diagonally dominant infinite matrices, invariant subspaces of operators on ℓ𝑝 to ℓ𝑞 spaces are shown. The global invertiblity of Sobolev spaces and functions on metric measure spaces with an interpolation are presented. The study of the regularity of the inverses of a planar Sobolev homemorphism and deformations with a finite surface energy are established and described widely. We find the iterates of a class of summation-type linear positive operators that preserving the affine functions, with an asymptotic behaviour and a partition of unity property.