Best approximation over the whole complex plane
نویسندگان
چکیده
منابع مشابه
Incomplete Rational Approximation in the Complex Plane
in certain natural regions in the complex plane where Pc, and q. are polynomials of degree cn and n, respectively. In particular we construct natural maximal regions (as a function of ~ and e) where the collection of such rational functions is dense in the analytical functions. So from this point of view we have rather complete analog theorems to the results concerning incomplete polynomials on...
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I show that the zeros of the chromatic polynomials PG(q) for the generalized theta graphs Θ(s,p) are, taken together, dense in the whole complex plane with the possible exception of the disc |q − 1| < 1. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) ZG(q, v) outside the disc |q + v| < |v|. An immediate corollary is that the chr...
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Given an open bounded set G in the complex plane and a weight function W (z) which is analytic and di erent from zero in G, we consider the problem of locally uniform rational approximation of any function f(z), which is analytic in G, by particular ray sequences of weighted rational functions of the form Wm+n(z)Rm;n(z), where Rm;n(z) = Pm(z)=Qn(z); with deg Pm m and degQn n: The main result of...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1982
ISSN: 0021-9045
DOI: 10.1016/0021-9045(82)90047-8