Asymptotic formulas for traces of Toeplitz matrices with symbols in
Hölder-Zygmund spaces
We discuss new higher order asymptotic formulas for traces of
Toeplitz matrices with symbols in Hölder-Zygmund spaces. Remainders
in these formulas go to zero with the speed depending on the
smoothness parameter of the space. The Wiener-Hopf factorization of
symbols within Hölder-Zygmund spaces plays an essential role in the
proof. These results refine Widom's asymptotic trace formulas and
complement Böttcher-Silbermann's higher order asymptotic formulas
for determinants of Toeplitz matrices.
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