  We study a system of pseudodifferential equations that is elliptic in the
sense of Petrovskii on a closed compact smooth manifold. We prove that the
operator generated by the system is Fredholm one on a refined two-sided scale
of the functional Hilbert spaces. Elements of this scale are the special
isotropic spaces of H\"{o}rmander--Volevich--Paneah.

Analysis of PDEs