Distribution in the sense of eigenvalues of [formula omitted]-Toeplitz sequences: Clustering and attraction

Abstract

This paper considers the spectral distribution and the concept of clustering and attraction in the sense of eigenvalues sequence of g-Toeplitz structures {Tn,g(f)} defined by Tn,g(f)=[fˆr−gs]r,s=0n−1, where g is a given nonnegative parameter, {fˆk} is the sequence of Fourier coefficients of the function f∈L1(Td) with T=(−π,π), d is a positive integer, and where f is real-valued and essentially bounded. A detailed treatment of the unilevel case is given, that is, d=1 and g∈N. The generalizations to the blocks and multilevel case are also presented for the case where g is a vector with nonnegative integer entries.