DOUGLIS-NIRENBERG ELLIPTIC SYSTEMS IN THE REFINED SCALE OF SPACES ON A CLOSED MANIFOLD

Dedicated to Professor Gorbachuk on the occasion of his 70th birthday. 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 Hörmander– Volevich–Paneah. The refined smoothness of a solution of the system is studied. The elliptic systems with a parameter are investigated as well. In this paper we consider Douglis-Nirenberg elliptic systems [1] of linear pseudodif-ferential equations on a smooth closed manifold. L. Hörmander [2, Sec. 1.0] proved a priori estimates for solutions of these systems in appropriate pairs of Sobolev spaces. These estimates are equivalent to the fact that the linear operator A corresponding to th