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The tensor product of frames.(Technical report)
- Article from:
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Sampling Theory in Signal and Image Processing
- Article date:
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January 1, 2008
- Author:
- Bourouihiya, Abdelkrim
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Copyright informationCOPYRIGHT 2008 Sampling Publishing. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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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.
Key words and phrases : Hilbert spaces, Tensor products, Frames, Riesz Bases.
2000 AMS Mathematics Subject Classification--Primary 42C15; Secondary 47A80.
1 Introduction
It is known that the tensor product of two orthonormal ...
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