Alexis Drouot - Maciej Zworski
A theorem proved by Quillen and by Catlin and D'Angelo states that a bi-homogeneous form on a multidimensional complex space which is positive away from zero can be written as a sum of squares of absolute values of polynomials once it is multiplied by the norm raised to a sufficiently high even power. In this note we provide a quantitative version of this theorem by giving an upper bound on the minimal power. This bound is roughly (n+m)^3 log(n), where n is the dimension and m the degree of the form.
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http://arxiv.org/abs/1205.3248
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