On Stability of Finitely Generated Shift-Invariant Systems

摘要

We consider the problem of completely characterizing when a system of integer translates in a finitely generated shift-invariant subspace of L_2(~d) is stable in the sense that rectangular partial sums for the system are norm convergent. We prove that a system of integer translates is stable in L_2(~d) precisely when its associated Gram matrix satisfies a suitable Muckenhoupt A_2 condition.