Parameter-elliptic operators on the extended Sobolev scale (Q2850444)

Parameter-elliptic equations constitute an important class of partial differential equations studied starting from the classical paper by \textit{M. S. Agranovich} and \textit{M. I. Vishik} [Usp. Mat. Nauk 19, No. 3(117), 53--161 (1964; Zbl 0137.29602)] to recent publications, such as \textit{R. Denk} and \textit{M. Faierman} [Integral Equations Oper. Theory 66, No. 3, 327--365 (2010; Zbl 1202.35077)]. In the paper under review, parameter-elliptic pseudodifferential operators on a closed smooth manifold are investigated on the extended Sobolev scale obtained by interpolation with functional smoothness index. These operators set isomorphisms between appropriate spaces of the scale. Two-sided a priori estimates of solutions are proved.