Fredholm Criteria for $G$-pseudodifferential Operators
Differential Geometry
2026-05-15 v1 Analysis of PDEs
Functional Analysis
Operator Algebras
Abstract
Let be a compact Lie group that acts smoothly on a closed manifold . Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of -pseudodifferential operators acting on Sobolev spaces of sections of vector bundles over . In case the group is finite, we obtain a further characterization of the Fredholm property of -pseudodifferential operators in terms of the invertibility of suitable symbols.
Cite
@article{arxiv.2605.14778,
title = {Fredholm Criteria for $G$-pseudodifferential Operators},
author = {Alexandre Baldare and Anton Yu. Savin and Elmar Schrohe},
journal= {arXiv preprint arXiv:2605.14778},
year = {2026}
}