Generalized locally Toeplitz sequences: Spectral analysis and applications to discretized partial differential equations (Q1874678)

Some generalizations of Toeplitz matrices and sequences thereof are considered: introduced are generalized locally Toeplitz sequences and multilevel locally Toeplitz sequences with the aim to characterize their asymptotic distribution of singular and eigenvalues using weighted multidimensional Szegő formulas. These results are of interest in connection with finite difference approximations of partial differential equations, with integral equations and with general orthogonal polynomials, and continue work done by the Serra Capizzana, Tili, Turtyshnikov and others.