  We introduce and investigate an adaptation of Fourier series to set-valued
functions (multifunctions, SVFs) of bounded variation. In our approach we
define an analogue of the partial sums of the Fourier series with the help of
the Dirichlet kernel using the newly defined weighted metric integral. We
derive error bounds for these approximants. As a consequence, we prove that the
sequence of the partial sums converges pointwisely in the Hausdorff metric to
the values of the approximated set-valued function at its points of continuity,
or to a certain set described in terms of the metric selections of the
approximated multifunction at a point of discontinuity. Our error bounds are
obtained with the help of the new notions of one-sided local moduli and
quasi-moduli of continuity which we discuss more generally for functions with
values in metric spaces.
