Block Toeplitz operators with frequency-modulated semi-almost periodic symbols

This paper is concerned with the influence of frequency modulation on the semi-Fredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphism α of the real line that ensure the following: if b belongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix functions) and the Toeplitz operator generated by the matrix function b(x) is semi-Fredholm, then the Toeplitz operator with the matrix symbol b(α(x)) is also semi-Fredholm.