Frames and Stable Bases for Shift-Invariant Subspaces of L2(Rd)

摘要

We study in this paper certain types of bases for shift-invariant subspaces ofL2(Rd). Our primary objective is to connect among three important families of basis sets: shift-invariant sets, Weyl-Heisenberg sets, and affine (wavelet) sets. The present paper is the first in a series of three, and is concerned with the basic theory of shift-invariant bases for shift-invariant spaces. The two other papers will focus on the applications of the theory developed here to Weyl-Heisenberg and affine sets.