کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772219 | 1413352 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Discrepancy densities for planar and hyperbolic zero packing
ترجمه فارسی عنوان
تراکم اختلاف برای بسته بندی صفر و فورمولار
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We study the problem of geometric zero packing, recently introduced by Hedenmalm [7]. There are two natural densities associated with this problem: the discrepancy density ÏH, given byÏH=liminfrâ1âinffâ¡â«D(0,r)((1â|z|2)|f(z)|â1)2dA(z)1â|z|2â«D(0,r)dA(z)1â|z|2 which measures the discrepancy in optimal approximation of (1â|z|2)â1 with the modulus of polynomials f, and its relative, the tight discrepancy density ÏHâ, which will trivially satisfy ÏHâ¤ÏHâ. These densities have deep connections to the boundary behaviour of conformal mappings with k-quasiconformal extensions, which can be seen from Hedenmalm's result that the universal asymptotic variance Σ2 is related to ÏHâ by Σ2=1âÏHâ. Here we prove that in fact ÏH=ÏHâ, resolving a conjecture by Hedenmalm in the positive. The natural planar analogues ÏC and ÏCâ to these densities make contact with work of Abrikosov on Bose-Einstein condensates. As a second result we prove that also ÏC=ÏCâ. The methods are based on Ameur, Hedenmalm and Makarov's Hörmander-type â¯-estimates with polynomial growth control [2]. As a consequence we obtain sufficiency results on the degrees of approximately optimal polynomials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 12, 15 June 2017, Pages 5282-5306
Journal: Journal of Functional Analysis - Volume 272, Issue 12, 15 June 2017, Pages 5282-5306
نویسندگان
Aron Wennman,