Rational approximation on certain plane sets
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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In functional neuroimaging, a crucial problem is to localize active sources within the brain non-invasively, from the knowledge of the electromagnetic measurements outside the head. Identi cation of point sources from boundary measurements is an ill-posed inverse problem. In the case of electroencephalography (EEG), measurements are only available at electrode positions, the number of sources i...
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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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For a function Ψ : R>0 → R>0, let Exact(Ψ) be the set of real numbers that are approximable by rational numbers to order Ψ, but to no order cΨ with 0 < c < 1. When Ψ is non-increasing and satisfies Ψ(x) = o(x−2), we establish that Exact(Ψ) has Hausdorff dimension 2/λ, where λ is the lower order at infinity of the function 1/Ψ. Furthermore, we study the set Exact(Ψ) when Ψ is not assumed to be n...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1969
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1969.29.631