The unitary extension principle for locally compact abelian groups with co-compact subgroups

The unitary extension principle by Ron and Shen is one of the cornerstones wavelet frame theory; it leads to tight frames for L 2 ( R stretchy="false">) L^{2}(\mathbb {R}) associated expansions functions alttext="f element-of f ∈ encoding="application/x-tex">f\in L^{2}(\mathbb similar type as those orthonormal bases. In this paper, extended setting a locally compact abelian group, equipped with collection nested co-compact subgroups. Unlike all previously known generalizations principle, current taking place within continuous frames, which means that resulting decompositions in underlying Hilbert space general are given terms integral representations rather than discrete sums. elements themselves appear letting modulation operators act on countable family basic functions.