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.
| Original language | American English |
|---|---|
| Pages (from-to) | 65-76 |
| Number of pages | 12 |
| Journal | Sampling Theory in Signal and Image Processing |
| Volume | 7 |
| Issue number | 1 |
| State | Published - Jan 1 2008 |
| Externally published | Yes |
ASJC Scopus Subject Areas
- Analysis
- Algebra and Number Theory
- Radiology Nuclear Medicine and imaging
- Computational Mathematics
Keywords
- Frames
- Hilbert spaces
- Riesz Bases
- Tensor Products
- Riesz bases
- Tensor products
Disciplines
- Mathematics
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