turkmath.org

In an attempt to identify the harmonic Drury-Arveson space, we introduce a whole new family of reproducing kernel Hilbert spaces of harmonic functions on the unit ball of R^n. We also define and derive basic properties of shift operators on these spaces. We show that the norm of one of these spaces is maximal among those with a certain type of reproducing kernel and on which the shifts are a row contraction. This is ongoing joint work with Daniel Alpay of Chapman University.