The Tensor Product of Frames
Sampling Theory in Signal and Image Processing
Hilbert spaces, Riesz Bases, Tensor Products, Frames
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.
Bourouihiya, Abdelkrim, "The Tensor Product of Frames" (2008). Mathematics Faculty Articles. 125.