On meromorphic approximation |
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Authors: | VA Prokhorov EB Saff |
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Institution: | (1) Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688-0002, USA;(2) Institute for Constructive Mathematics, Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA |
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Abstract: | Let G be a bounded N-connected domain, the boundary of which consists of closed analytic Jordan curves. We assume that 0G. For any nonnegative integers n and m, denote by
n,m
the class of all meromorphic functions on G that can be represented in the form h=p/qz
m
, where p belongs to the Smirnov class E
(G), q is a polynomial of degree at most n, q0. Theorems giving necessary and sufficient conditions for a function belonging to the class
n,m
to be an element of best approximation to a continuous function f on in the space L
() by functions in the class
n,m
are proved. Some questions concerning orthogonal polynomials and the theory of Hankel operators are also considered. |
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Keywords: | meromorphic approximation best approximation Hankel operator singular numbers orthogonal polynomials |
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