The Structure of Finitely Generated Shift-Invariant Subspaces in Super Hilbert Spaces

Abstract

We study the structure of finitely generated shift-invariant subspaces with generators from the super Hilbert space L ²(ℝ ^d )^(N). We give a characterization for these subspaces. Moreover, we show that every finitely generated shift-invariant subspace possesses a tight frame. We also give a necessary and sufficient condition for such a space to be principal. Our results generalize similar ones for which generators are from L ²(ℝ ^d ).

Keywords:

• Frames
• Shift-invariant subspaces
• Super Hilbert spaces

Mathematics Subject Classification:

• 42C15
• 42C40
• 41A58

ACKNOWLEDGMENTS

This work was supported partially by the National Natural Science Foundation of China (10971105 and 10990012) and the Natural Science Foundation of Tianjin (09JCYBJC01000).