A characterization of MG Dual frames using infimum cosine angle

TL;DR

This paper characterizes dual frames in multiplication generated systems on $L^2$ spaces using infimum cosine angles, providing necessary and sufficient conditions and illustrating with translation-generated systems on non-abelian groups.

Contribution

It introduces a new characterization of dual frames via infimum cosine angles for multiplication generated frames, including conditions for their uniqueness.

Findings

Derived necessary and sufficient conditions for dual frames using infimum cosine angles.

Established the uniqueness criteria for dual frames in this setting.

Applied the theoretical results to translation-generated systems on non-abelian groups.

Abstract

This article discusses the construction of dual frames and their uniqueness for the multiplication generated frames on $L^2(X; \mathcal H)$, where $X$ is a $\sigma$-finite measure. A necessary and sufficient condition of such duals associated to infimum cosine angle is obtained. The result is illustrated for the translation-generated systems on a locally compact group (not necessarily abelian ) by action of its abelian subgroup.