Fredholm theory connected with a Douglis-Nirenberg system of differential equations over R^n - Faierman, M. (Methods of Functional Analysis and Topology, 2016)
We consider a spectral problem over R^n for a Douglis-Nirenberg system of differential operators under limited smoothness assumptions and under the assumption of parameter-ellipticity in a closed sector L in the complex plane with vertex at the origin. We pose the problem in an L_p Sobolev-Bessel potential space setting, 1 < p < ∞, and denote by A_p the operator induced in this setting by the spectral problem. We then derive results pertaining to the Fredholm theory for A_p for values of the spectral parameter λ lying in L as well as results pertaining to the invariance of the Fredholm domain of A_p with p.