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Kolmogorov problem on widths asymptotics and pluripotential theory
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sabanci, V. Zakharyuta Babenko, Zahariuta Levin-Tikhomirov, Widom Nguyen, S. Fisher-Miccheli |
| Copyright Year | 2006 |
| Abstract | Given a compact setK in an open setD on a Stein manifold ; dim = n; the set AK of all restrictions of functions, analytic in D with absolute value bounded by 1; is a compact subset of C(K). The problem on the strict asymptotics for Kolmogorov diameters (widths) : ln ds AK s; s!1: was stated by Kolmogorov in an equivalent formulation for "-entropy of that set [13, 14, 16]. It was conjectured in [46, 47] that for "good" pairs (K;D) such an asymptotics holds with the constant = 2 n! C(K;D) 1=n , where C (K;D) is the pluricapacity of the "pluricondenser" (K;D), introduced by Bedford-Taylor [6]. In the one-dimensional case it is equivalent to Kolmogorovs conjecture about the "-entropy of the set AK , which has been con rmed by e¤orts of many authors (Erokhin, Babenko, Zahariuta, Levin-Tikhomirov, Widom, Nguyen, Skiba Zahariuta, Fisher Miccheli, et al). In [46, 47] the above problem had been reduced (the proof was only sketched there) to the certain problem of pluripotential theory about approximating of the relative Green pluripotential of the "pluricondenser" (K;D) by pluripotentials with nite set of logarithmical singulatities. The latter problem has been solved recently by Poletsky [25] and Nivoche [23, 24]. Here we give a detailed proof of the above-mentioned reduction, which provides, together with the Nivoche-Poletsky result, a positive solution of our conjecture about asymptotics of Kolmogorov diameters. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://research.sabanciuniv.edu/7149/1/stvkaf01841.pdf |
| Alternate Webpage(s) | http://research.sabanciuniv.edu/7149/2/kpwa2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Diameter (qualifier value) Fisher information Naruto Shippuden: Clash of Ninja Revolution 3 Subgroup manifold |
| Content Type | Text |
| Resource Type | Article |
