Characterizations of Translation Generated Dual Frames Using Infimum Cosine Angle

Abstract

This article discusses the existence conditions of dual frames and their uniqueness for the Γ-translation generated frames systems in L2(G), where G be a locally compact group, and Γ is a closed abelian subgroup of G. Necessary and sufficient conditions of such duals associated with the infimum cosine angles are obtained. The problems are first addressed in the context of multiplication-generated frame systems in L2(X

H), where X is a σ-finite measure space, then obtained the results for locally compact group setups. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.