تقرير
Interpolation by multivariate polynomials in convex domains
| العنوان: | Interpolation by multivariate polynomials in convex domains |
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| المؤلفون: | Antezana, Jorge, Marzo, Jordi, Ortega-Cerdà, Joaquim |
| المصدر: | Comput. Methods Funct. Theory 21 (2021), no. 4, 831-849 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs |
| الوصف: | Let $\Omega$ be a convex open set in $\mathbb R^n$ and let $\Lambda_k$ be a finite subset of $\Omega$. We find necessary geometric conditions for $\Lambda_k$ to be interpolating for the space of multivariate polynomials of degree at most $k$. Our results are asymptotic in $k$. The density conditions obtained match precisely the necessary geometric conditions that sampling sets are known to satisfy, and they are expressed in terms of the equilibrium potential of the convex set. Moreover, we prove that in the particular case of the unit ball, for $k$ large enough, there is no family of orthogonal reproducing kernels in the space of polynomials of degree at most $k$. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s40315-021-00410-8 |
| URL الوصول: | http://arxiv.org/abs/2101.08064 |
| رقم الأكسشن: | edsarx.2101.08064 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s40315-021-00410-8 |
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