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Can a positive polynomial on sphere be represented as the sum of squares of spherical harmonics

This Wikipedia page has many references: https://en.wikipedia.org/wiki/Positive_polynomial, including for example Marshall, Murray Positive polynomials and sums of squares. Mathematical Surveys and …
Zach Teitler's user avatar
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1 vote

The relationship between the symmetric tensor product and sum of squares

No, it's not true. First of all, if $V$ is a vector space spanned by monomials of some degree $d$, then $V$ is a vector space of (homogeneous) polynomials (of degree $d$). Then $\operatorname{Sym}^2(V …
Zach Teitler's user avatar
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