Report
Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Characterization of polynomials by L2-estimates
| العنوان: | Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Characterization of polynomials by L2-estimates |
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| المؤلفون: | Magnússon, Benedikt Steinar, Sigurðardóttir, Álfheiður Edda, Sigurðsson, Ragnar, Snorrason, Bergur |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, 32U35 (Primarey) 32A08, 32A15, 32U15, 32W50 (Secondary) |
| الوصف: | The main result of this paper is that an entire function $f$ that is in $L^2(\mathbb C^n,\psi)$ with respect to the weight $\psi(z)=2mH_S(z)+\gamma\log(1+|z|^2)$ is a polynomial with exponents in $m\widehat S_\Gamma$. Here $H_S$ is the logarithmic supporting function of a compact convex set $S\subset \mathbb R^n_+$ with $0\in S$, $\gamma\geq 0$ is small enough in terms of $m$, and $\widehat S_\Gamma$ is the hull of $S$ with respect to a certain cone $\Gamma$ depending on $S$, $m$ and $\gamma$. An example showing that in general $\widehat S_\Gamma$ can not be replaced by $S$ is constructed. Comment: 7 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.06847 |
| رقم الانضمام: | edsarx.2305.06847 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |