Distribution results on the algebra generated by Toeplitz sequences: a finite-dimensional approach Original Research Article

Let a be an L1 symbol defined on Qd, Q=(−π,π) with dgreater-or-equal, slanted1 and let us consider the multi-indexed sequence of Toeplitz matrices {Tn(a)} with nset membership, variantNd. It is well known that {Tn(a)} is spectrally distributed as a in the sense of the singular values. In this paper we prove that a sequence as {∑α∏βTn(aαβ)} is spectrally distributed in the sense of the singular values as the measurable function θ=∑α∏βaαβ for aαβset membership, variantL1 and α and β ranging in any finite set of values.