Abstract. We study the asymptotic properties of Stieltjes polynomials outside the support of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markov-type functions. An estimate for the speed of convergence of Gauss-Kronrod quadrature formula in the case of analytic functions is also given.
: Given a measure /^oj the unit circle T whose weight funotion w satisfies log w E L (T), we characterize the dou ly and simply invariant subspaces for the shift operator on L 1 (,k') 1z pzco . In particular, Szego's theorem appears when p=2, and like in the classical case, HP(~,,,) can be factorized as the pro duct of inner and %^c-outer fúnctions .
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