Toeplitz eigenvalues for Radon measures

Abstract

It is well known that for Toeplitz matrices generated by a "sufficiently smooth" real-valued symbol, the eigenvalues behave asymptotically as the values of the symbol on uniform meshes while the singular values, even for complex-valued functions, do as those values in modulus. These facts are expressed analytically by the Szegö and Szegö-like formulas, and as is proved recently, the "smoothness" assumptions are as mild as those of L_{1}. In this paper, it is shown that the Szegö-like formulas hold true even for Toeplitz matrices generated by the so-called Radon measures.