NORMS OF TOEPLITZ MATRICES WITH FISHER-HARTWIGSYMBOLS

摘要

We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the ease of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long range memory.