Balayage and convergence of rational interpolants (Q1305495)

The authors charaterize those regions for which one can find a table of interpolation points and a table of prescribed poles such that for any analytic function on the region the corresponding sequence of interpolating rational functions with prescribed poles converges to the given function. The problem is reduced to that of determining how must a region be so that one can find measures supported on either sides of its boundary such that their balayage onto the boundary coincides.