We provide a new method to approximate (possibly discontinuous) function using Christoffel–Darboux kernels. Our knowledge about the unknown multivariate is in terms of finitely many moments Young measure supported on graph function. Such an input available when approximating weak (or measure-valued) solution optimal control problems, entropy solutions nonlinear hyperbolic PDEs, or numerical int...

We consider the global minimization of a polynomial on compact set $$\mathbf {B}$$ . show that each step Moment-SOS hierarchy has nice and simple interpretation complements usual one. Namely, it computes coefficients in an orthonormal basis $$L^2(\mathbf {B},\mu )$$ where $$\mu $$ is arbitrary reference measure whose support exactly The resulting certain density (with respect to ) some signed W...