P-FRAMES FOR BANACH SPACES ON LOCALLY COMPACT AEOLIAN GROUPS

摘要

We define a shift invariant closed linear subspace B_Φ(G)of a solid Banach function Space on a locally compact abelian group G and obtain necessary and sufficient conditions for a set of translates (T_(λ,Φ))_(λ∈Λ),Φ ∈ W(L~p,l_w~1), to constitute a frame for it, Λ being a lattice in G. Although motivated from the work of Aldroubi, Sun and Tang [AST 01], the main result of this paper (Theorem 4.1) is an independent and more general result in this line of work. This papers paves the way for the study of p-frames and related topics for various types of Banach spaces of functions or distributions defined on locally compact groups.