Since Approximation Theory is already there …Bring Potential Theory to Operator Theory!

The purpose of the talk is to discuss, by presenting a number of concrete examples, the luck of application of Potential Theory tools in Operator Theory. More precisely, results from the theory of subharmonic functions (like the maximum principle, the principle of descent, the lower envelope theorem, the unicity theorem and Carleson unicity theorem) have been used extensively in order to study the behaviour of extremal, or orthogonal polynomials, in Approximation Theory. Such results, as powerful as they are, have not found their way to the study of spectral properties of certain important operators, given that the eigenvalues of finite central truncations of these operators are, simply, the zeros of associated orthogonal polynomials.