On p-dependent local spectral properties of certain linear differential operators in $L^{p}(ℝ^{N})$
Volume 130 / 1998
Fundamenta Mathematicae 130 (1998), 23-52
DOI: 10.4064/sm_1998_130_1_1_23_52
Abstract
The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in $L^p(ℝ^N)$. The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is achieved via a combination of methods from the theory of Fourier multipliers and local spectral theory.
