Rational Approximation of Analytic Functions Having Generalized Orders of Rate of Growth |
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Authors: | V.A. Prokhorov |
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Affiliation: | (1) Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, 36688-0002 |
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Abstract: | Let f be holomorphic on a domain G C¯ and n be the error in best approximation of f in the supremum norm on a compact set E G by rational functions of order n. We obtain results characterizing the degree of decrease of the best approximation n in terms connected with the condenser (E,F), F=C¯ G¯, and the rate of growth of the maximum modulus of f(z). In particular, if f has a generalized order (, , f) in the domain G, thenlim supn (n)/ (log (1/log+((0 1 ....... n)1/n(n+1) ))) (, , f),where = exp (1/C(E,F)), C(E,F) is the capacity of the condenser (E,F). |
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Keywords: | Rational approximation analytic functions Hankel operator singular numbers |
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