SPECTRAL FEATURES AND ASYMPTOTIC PROPERTIES FOR g-CIRCULANTS AND g-TOEPLITZ SEQUENCES

摘要

For a given nonnegative integer g, a matrix A(n) of size n is called g-Toeplitz if its entries obey the rule A(n) = [a(r-gs)](r,s=0)(n-1). Analogously, a matrix A(n) again of size n is called g-circulant if A(n) = [a((r-gs) mod n)](r,s=0)(n-1). Such matrices arise in wavelet analysis, subdivision algorithms, and more generally when dealing with multigrid/multilevel methods for structured matrices and approximations of boundary value problems. In this paper we study the singular values of g-circulants and provide an asymptotic analysis of the distribution results for the singular values of g-Toeplitz sequences in the case where {a(k)} can be interpreted as the sequence of Fourier coefficients of an integrable function f over the domain (-pi, pi). Generalizations to the block and multilevel case are also considered.