关于半正定多项式的坏点
On the bad points of positive semidefinite polynomials
摘要：
一个半正定实多项式f的坏点是一个极点出现在f的所有表达式中作为有理函数的平方和的点。我们证明了三元四次多项式永远不会有坏点。我们给出的例子，正半定多项式的一个坏点在原点，但总和平方正式幂级数，回答一个问题的Brumfiel。我们还给出了一个例子，一个半正定多项式在三个变量与复杂的坏点，这是不真实的，回答一个问题的Scheiderer。
英文摘要：
A bad point of a positive semidefinite real polynomial f is a point at which a pole appears in all expressions of f as a sum of squares of rational functions. We show that quartic polynomials in three variables never have bad points. We give examples of positive semidefinite polynomials with a bad point at the origin, that are nevertheless sums of squares of formal power series, answering a question of Brumfiel. We also give an example of a positive semidefinite polynomial in three variables with a complex bad point that is not real, answering a question of Scheiderer.
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