Mathematics Faculty Articles

Title

The Tensor Product of Frames

Document Type

Article

Publication Date

1-1-2008

Publication Title

Sampling Theory in Signal and Image Processing

Keywords

Hilbert spaces, Riesz Bases, Tensor Products, Frames

ISSN

1530-6429

Volume

7

Issue/No.

1

First Page

65

Last Page

76

Abstract

In this paper we prove that the tensor product of two sequences is a frame (Riesz basis) if and only if each part of this product is a frame (Riesz basis). Using this result, we extend some density and sampling theorems to higher dimensions. To prove the part of our main result concerning Riesz bases, we prove that the tensor product of two bounded operators is invertible only if each part of this product is invertible.

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