Uncertainty principles for magnetic structures on certain coadjoint orbits

TL;DR

This paper extends uncertainty principles to magnetic structures on specific coadjoint orbits of infinite-dimensional Lie groups, connecting Heisenberg inequalities and ambiguity functions with magnetic Weyl calculus.

Contribution

It develops new uncertainty principles for magnetic structures on coadjoint orbits of infinite-dimensional Lie groups, generalizing magnetic Weyl calculus.

Findings

Established uncertainty principles for magnetic structures on coadjoint orbits.

Connected Heisenberg inequalities with magnetic ambiguity functions.

Unified magnetic Weyl calculus for abelian and non-abelian groups.

Abstract

By building on our earlier work, we establish uncertainty principles in terms of Heisenberg inequalities and of the ambiguity functions associated with magnetic structures on certain coadjoint orbits of infinite-dimensional Lie groups. These infinite-dimensional Lie groups are semidirect products of nilpotent Lie groups and invariant function spaces thereon. The recently developed magnetic Weyl calculus is recovered in the special case of function spaces on abelian Lie groups.