Positive Semidefinite Analytic Functions on Real Analytic Surfaces

Let $$X\subset {\mathbb {R}}^n$$ be a (global) real analytic surface. Then every positive semidefinite meromorphic function on X is a sum of 10 squares of meromorphic functions on X. As a consequence, we provide a real Nullstellensatz for (global) real analytic surfaces.

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