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- W1604214939 abstract "Let w(θ) be a positive weight function on the unit circle of the complex plane. For a sequence of points { αk }k = 1∞ included in a compact subset of the unit disk, we consider the orthogonal rational functions φn that are obtained by orthogonalization of the sequence { 1, z / π1, z2 / π2, ... } where ( {pi }_k left( {rm Z} right) = prodnolimits_{j^{ = 1} }^k {left( {1 - overline {alpha } j{rm Z}} right)} ), with respect to the inner product (leftlangle {f,g} rightrangle = frac{1}{{2{pi }}}int_{{ - pi }}^{pi } {fleft( {{e}^{itheta } } right)} overline {gleft( {{e}^{itheta } } right)} wleft( {theta } right){dtheta }) In this paper we discuss the behaviour of φn(t) for ∣ t ∣ = 1 and n → ∞ under certain conditions. The main condition on the weight is that it satisfies a Lipschitz–Dini condition and that it is bounded away from zero. This generalizes a theorem given by Szegő in the polynomial case, that is when all αk = 0." @default.
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- W1604214939 doi "https://doi.org/10.1023/a:1006409205633" @default.
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