Szego Seminar: "Model Formulas on the Disk and Bidisk"

Mark Mancuso, Washington University in Saint Louis

Abstract: The multiplier algebra of the classical Hardy space $H^2$ on the open unit disk is isometrically isomorphic to $H^{\infty}$, the bounded holomorphic functions on the disk. This allows us to prove that elements of the unit ball of $H^{\infty}$ solve the Nevanlinna-Pick interpolation problem. By introducing the concept of model formulas, we are able to show a realization formula holds for such functions, and can therefore deduce that whenever the Pick matrix is positive semi-definite, there is an interpolating function in the unit ball of $H^{\infty}$. Time permitting, we will discuss the corresponding objects in the case of the bidisk and explain how some ideas carry over from the disk case relatively simply, but the key is the Ando dilation theorem for two commuting contractions.

Host: Christopher Felder