Representations of homogeneous polynomials as a sum of powers of linear forms with restricted support

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• 作者：E. Ballico (1)
  
  1. Department of Mathematics ; University of Trento ; 38123 ; Povo (TN) ; Italy
  
• 关键词：symmetric tensor rank ; Veronese embedding ; Power sum decomposition ; Multivariate polynomials ; 14N05 ; 15A69
• 刊名：Rendiconti del Circolo Matematico di Palermo
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：64
• 期：1
• 页码：1-25
• 全文大小：397 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Geometry
  Analysis
  Applications of Mathematics
  
• 出版者：Springer Milan
• ISSN：1973-4409

文摘

We study the decomposition of a degree \(d\) homogeneous linear form \(f\in K[x_0,\dots ,x_n]\) as a sum of \(x\) \(d\) -powers of linear forms in \(x_0,\dots ,x_n\) and \(y\) \(d\) -powers of \(x_1,\dots ,x_n\) . Most of our results are for cases with \(ny \le \left( {\begin{array}{c}n+d-1\\ n-1\end{array}}\right) \) and with \(d\ge 5\) . If \(n\le 4\) , we also consider the cases \(d=3,4\) . We also study other interpolation problems (e.g., flags instead of a hyperplane).