Multilevel symmetrized toeplitz structures and spectral distribution results for the related matrix sequences∗

In recent years, motivated by computational purposes, the singular value and spectral features of the sym-metrization of Toeplitz matrices generated by a Lebesgue integrable function have been studied. Indeed, under the assumptions that f belongs to L1 ([−π, π]) and it has real Fourier coefficients, the spectral and singular value distribution of the matrix-sequence {YnTn[f]}n has been identified, where n is the matrix size, Yn is the anti-identity matrix, and Tn[f] is the Toeplitz matrix generated by f. In this note, the authors consider the multilevel Toeplitz matrix Tn[f] generated by f ∈ L1 ([−π, π]k ), n being a multi-index identifying the matrix-size, and they prove spectral and singular value distribution results for the matrix-sequence {YnTn[f]}n with Yn being the corresponding tensorization of the anti-identity matrix.