  Recently A. Eremenko and P. Yuditskii found explicit solutions of the best
polynomial approximation problems of sgn(x) over two intervals in terms of
conformal mappings onto special comb domains. We give analogous solutions for
the best approximation problems of sgn(x) over two symmetric intervals by odd
rational functions with fixed poles. Here the existence of the related
conformal mapping is proved by using convexity of the comb domains along the
imaginary axis.
