Physical Sciences and Mathematics Commons^™

Hankel Operators On The Drury-Arveson Space, James Allen Sunkes Iii

Doctoral Dissertations

The Drury-Arveson space, initially introduced in the proof of a generalization of von Neumann's inequality, has seen a lot of research due to its intrigue as a Hilbert space of analytic functions. This space has been studied in the context of Besov-Sobolev spaces, Hilbert spaces with complete Nevanlinna Pick kernels, and Hilbert modules. More recently, McCarthy and Shalit have studied the connections between the Drury-Arveson space and Hilbert spaces of Dirichlet series, and Davidson and Cloutare have established analogues of classic results of the ball algebra to the multiplier algebra for the Drury-Arveson Space.

The goal of this dissertation is …