The CD-kernel is an old and well known tool in theory of approximation and orthogonal polynomials. It turns out that it can provide an efficient and easy to use tool to address some problems in data analysis (e.g., outlier detection, support inference, density approximation, etc.) where the measure of interest is discrete (its support is the cloud of data points to analyse). In addition it can also be used in other applications:

• Interpolate functions from a sample of its values;
• Recover a function from moments of the measure supported on its graph (which is typically the information obtained as output of the Moment-SOS hierarchy in dynamical systems).

Finally, the CD-kernel is also involved in an interpretation of the Moment-SOS Hierarchy in polynomial optimization as well as in results on its rate of convergence.