The geometry of sampling on unions of lattices
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- by Eric Weber PDF
- Proc. Amer. Math. Soc. 132 (2004), 3661-3670 Request permission
Abstract:
In this paper we show two results concerning sampling translation-invariant subspaces of $L^2({\mathbb R}^d)$ on unions of lattices. The first result shows that the sampling transform on a union of lattices is a constant times an isometry if and only if the sampling transform on each individual lattice is so. The second result demonstrates that the sampling transforms of two unions of lattices on two bands have orthogonal ranges if and only if, correspondingly, the sampling transforms of each pair of lattices have orthogonal ranges. We then consider sampling on shifted lattices.References
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Additional Information
- Eric Weber
- Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036
- Address at time of publication: Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, Iowa 50011
- MR Author ID: 660323
- Email: esweber@iastate.edu
- Received by editor(s): November 4, 2002
- Received by editor(s) in revised form: August 26, 2003
- Published electronically: June 21, 2004
- Additional Notes: This research was supported in part by NSF grants DMS-0200756 and DMS-0308634.
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3661-3670
- MSC (2000): Primary 42B05; Secondary 94A20
- DOI: https://doi.org/10.1090/S0002-9939-04-07588-4
- MathSciNet review: 2084089