ABSTRACT. We prove that the well-known interpolation conditions for rational approximations with free poles are not sufficient for finding a rational function of the least deviation. For rational approximations of degree (k, 1), we establish that these interpolation conditions are equivalent to the assertion that the interpolation point c is a stationary point of the function ~k(c) defined as the squared deviation of / from the subspace of rational functions with numerator of degree _< k and with a given pole 1]~. For any positive integers k and s, we construct a function g E H2C D) such that Rt,x(g) ----Rk+m,l(g) > 0, where Rk,l(g) is the least deviation of g from the class of rational function of degree _< (k, 1).
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