Rational functions of best uniform approximation and holomorphic continuation of functions |
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Authors: | I V Ivanov R K Kovacheva J Gilewicz |
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Institution: | (1) CNRS Luminy case 907 CPT, F 13288 Marseille Cedex 9, France;(2) Institute of Mathematics, Bulgarian Academy of Sciences, Bulgarian |
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Abstract: | Let f be a function, continuous and real valued on the segment Δ, Δ ⊂ (−∞, ∞) and {Rn} be the sequence of the rational functions of best uniform approximation to f on Δ of order (n, n). In the present work,
the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zero capacity.
As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of f are given.
The work is supported by Project 69 with Ministry of Science and Education, Bulgaria. |
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Keywords: | |
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