Higher order asymptotic formulas for Toeplitz matrices with symbols in generalized H\"older spaces

We prove higher order asymptotic formulas for determinants and traces of finite block Toeplitz matrices generated by matrix functions belonging to generalized H"older spaces with characteristic functions from the Bari-Stechkin class. We follow the approach of B"ottcher and Silbermann and generalize their results for symbols in standard H"older spaces.