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Journal of Function Spaces
Volume 2016, Article ID 4573940, 14 pages
http://dx.doi.org/10.1155/2016/4573940
Research Article

Modeling Sampling in Tensor Products of Unitary Invariant Subspaces

1Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911 Madrid, Spain
2Departamento de Matemáticas Fundamentales, U.N.E.D., Senda del Rey 9, 28040 Madrid, Spain

Received 25 July 2016; Accepted 16 October 2016

Academic Editor: Hans G. Feichtinger

Copyright © 2016 Antonio G. García et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The use of unitary invariant subspaces of a Hilbert space is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of and also periodic extensions of finite signals are remarkable examples where this occurs. As a consequence, the availability of an abstract unitary sampling theory becomes a useful tool to handle these problems. In this paper we derive a sampling theory for tensor products of unitary invariant subspaces. This allows merging the cases of finitely/infinitely generated unitary invariant subspaces formerly studied in the mathematical literature; it also allows introducing the several variables case. As the involved samples are identified as frame coefficients in suitable tensor product spaces, the relevant mathematical technique is that of frame theory, involving both finite/infinite dimensional cases.