Globally solvable complexes of pseudo-differential operators on the torus

TL;DR

This paper investigates the conditions under which a complex of pseudo-differential operators on the torus is globally solvable, linking it to the solvability of its normal form, especially for systems with constant coefficients.

Contribution

It provides a characterization of global solvability for such complexes and connects it to the solvability of their normal forms, advancing understanding in pseudo-differential operator theory.

Findings

Characterization of global solvability for complexes with constant coefficients

Connection established between solvability of the complex and its normal form

Insights into the structure of pseudo-differential operators on the torus

Abstract

We consider a complex of pseudo-differential operators associated with an overdetermined system of operators defined on the torus. We characterize the global solvability of this complex when the system has constant coefficients. Furthermore, we establish some connections between the global solvability of the complex and the global solvability of its normal form.