Douglis-Nirenberg elliptic systems in the refined scale of spaces on a closed manifold

Abstract

Douglis-Nirenberg elliptic systems of linear pseudodifferential equations are studied on a smooth closed manifold. We prove that the operator generated by the system is a Fredholm one on the refined two-sided scale of the functional Hilbert spaces. Elements of this scale are the special isotropic spaces of H\"{o}rmander--Volevich--Paneah. The refined smoothness of a solution of the system is studied. The elliptic systems with a parameter are investigated as well.