Some concrete aspects of Hilbert's 17th Problem
Some concrete aspects of Hilbert's 17th Problem
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DOI：
10.1090/conm/253/03936
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
B. Reznick
中科院分区：
文献类型：
--
作者：
B. Reznick
希尔伯特（Hilbert）的第17个问题询问，在几个变量中，真正的阳性半黑成（PSD）多项式是否必须是理性函数的正方形总和。本文对文献进行了有关两个密切相关问题的文献调查：关于PSD多项式不是多项式正方形的PSD多项式的说法？一个人如何将给定的PSD多项式作为理性函数的正方形总和？这些问题可以追溯到希尔伯特本人，他对他们的兴趣早于1900年的巴黎国会大会。
Hilbert's 17th Problem asks whether a real positive semide nite (psd) polynomial in several variables must be a sum of squares of rational functions. This paper gives a survey of the literature on two closely related questions: What can be said about a psd polynomial that is not a sum of squares of polynomials? How can one write a given psd polynomial as a sum of squares of rational functions? These questions go back to Hilbert himself, and his interest in them predated the 1900 Paris Congress.