Elliptic systems of pseudodifferential equations in a refined scale on a closed manifold

TL;DR

This paper investigates elliptic pseudodifferential systems on closed manifolds, demonstrating that the associated operator is Fredholm on a specialized refined scale of isotropic Hilbert spaces, extending classical results.

Contribution

It establishes the Fredholm property of elliptic pseudodifferential systems within a refined isotropic scale on closed manifolds, using Hörmander–Volevich–Paneah spaces.

Findings

Operator is Fredholm on the refined scale

Extension of elliptic theory to specialized isotropic spaces

Provides a framework for analyzing elliptic systems in advanced functional spaces

Abstract

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.