QTT-rank-one vectors with QTT-rank-one and full-rank Fourier images (Q417446)

The class of rank-one vectors with rank-one Fourier images is described. Also an example of a rank-one vector that has full-rank Fourier image is given. This shows that the Fourier transform is a nontrivial operation that can increase quantics tensor train (QTT) ranks of a vector to the maximum. Finally, by numerical experiments the author shows that practical \(\varepsilon\)-ranks of Fourier images of certain rank-one vectors (including the randomly distributed vectors) are moderate even for vectors of very large mode sizes.