Modeling Sampling in Tensor Products of Unitary Invariant Subspaces. (30th November 2016)

• Record Type: Journal Article
• Authors: García, Antonio G.; Ibort, Alberto; Muñoz-Bouzo, María J.
• Other Names: Feichtinger Hans G. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-11-30
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/4573940
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The use of unitary invariant subspaces of a Hilbert space H is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of L 2 ( R ) 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.