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A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
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Let $S_{E}$ be the shift operator on vector-valued Hardy space $H_{E}^{2}.$ Beurling-Lax-Halmos Theorem identifies the invariant subspaces of $S_{E}$ and hence also the invariant subspaces of the backward shift $S_{E}^{\ast}.$ In this…