Abstract
The Laurent projection in the space of functions analytic in an annulus and continuous on its boundary is shown to be minimal with respect to the minimax norm. The problem of polynomial interpolation of continuous complex-valued functions in the unit disc with nodes on the boundary is also studied. In case the number of nodes is odd, the Erdös conjecture is proved, viz, that the polynomial projection, induced by interpolation at the equally distributed nodes on the unit circle, is optimal in the sense of the sup-norm.
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