Fredholm theory connected with a Douglis-Nirenberg system of differential equations over R^n

Abstract: 

We consider a spectral problem over RnRn for a Douglis-Nirenberg system of differential operators under limited smoothness asumptions as well as under the assumption of parameter-ellipticity in a closed sector LL in the complex plane with vertex at the origin. We pose the problems in a LpLp Sobolev-Bessel potential space setting, 1<p<∞1<p<∞, and denote by ApAp the operator induced in this setting by the spectral problem. We then derive results pertaining to the Fredholm theory for ApAp for values of the spectral parameter λλ lying in LL as well as results pertaining to the invariance of the Fredholm domain of ApAp with pp.