Elenco seminari del ciclo di seminari
“COMPLEX ANALYSIS LAB”

If H is a space of functions defined on some set X, evaluating functions at those points provides additional structure to the space H. If the evaluation functionals are bounded on H, we call the overall structure a Reproducing Kernel Hilbert Space (RKHS). This viewpoint goes back to the early XX century, and it was axiomatized in the early 50's by Bergman and Aronszsajn. In this seminar lecture we want to lay down the basics of the theory as in the seminal article od Aronszajn and provide some examples. In forthcoming seminar, we will explore problems of interpolation in RKHS.

PhD thesis defense

We close the characterization of the Carleson measures for the Dirichlet space by giving one (perhaps two) solution(s) to the corresponding dyadic problem.

In this series of expository talks we introduce and discuss tools of ergodic theory such as recurrence theorems in order to give the proof of Szemeredi’s theorem.

We give a description of the zero set intersection the unit sphere of a zero-free polynomial in the unit ball of Cn. The nice description leads to the formulation of a conjecture regarding the characterization of polynomials that are cyclic in Dirichlet-type spaces in the unit ball of Cn. Furthermore, we answer partially ascertaining whether an arbitrary polynomial is not cyclic.