On the structure and properties of lower bounded analytic frames

Abstract

Algebraic frames are generalizations of Fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unbounded linear functionals. The paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discreteness and the redundancy of the frame family.