On the effective Putinar’s Positivstellensatz and moment approximation

We analyse the representation of positive polynomials in terms Sums Squares. provide a quantitative version Putinar’s Positivstellensatz over compact basic semialgebraic set S, with new polynomial bound on degree positivity certificates. This involves Łojasiewicz exponent associated to description S. show that if gradients active constraints are linearly independent S (Constraint Qualification condition), this is equal 1. deduce first general convergence rate optima Lasserre’s Sum-of-Squares hierarchy global optimum function and Hausdorff distance between cone truncated (probability) measures supported pseudo-moment sequences, which quadratic module