  In this paper we use recently developed calculus of residue currents together
with integral formulas to give a new explicit analytic realization, as well as
a new analytic proof of Serre duality on any reduced pure $n$-dimensional
paracompact complex space $X$. At the core of the paper is the introduction of
concrete fine sheaves $\mathscr{B}_X^{n,q}$ of certain currents on $X$ of
bidegree $(n,q)$, such that the Dolbeault complex
$(\mathscr{B}_X^{n,\bullet},\,\bar{\partial})$ becomes, in a certain sense, a
dualizing complex. In particular, if $X$ is Cohen-Macaulay (e.g., Gorenstein or
a complete intersection) then $(\mathscr{B}_X^{n,\bullet},\,\bar{\partial})$ is
an explicit fine resolution of the Grothendieck dualizing sheaf.
