Fat diagonals and Fourier analysis

We use Fourier analysis and Toeplitz matrices to study the effect on matrix norms obtained by various "truncations" of the matrix. Examples include the truncation of a matrix to a central band of diagonals, truncation to the off-diagonal part, and the upper-triangular truncation. Our tools include tensor product constructions, asymptotic eigenvalue distributions, and multilevel Toeplitz matrices.