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Using standard tools of harmonic analysis, we state and solve the problem ofmoments for positive measures supported on the unit ball of a Sobolev space ofmultivariate periodic trigonometric functions. We describe outer and innersemidefinite approximations of the cone of Sobolev moments. They are the basiccomponents of an infinite-dimensional moment-sums of squares hierarchy,allowing to solve numerically non-convex polynomial optimization problems oninfinite-dimensional Sobolev spaces, with global convergence guarantees.

Solving moment and polynomial optimization problems on Sobolev spaces