Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions

Daniel Alpay, Foster G. and Mary McGaw Professorship in Mathematical Sciences, Chapman UniversityFabrizio Colombo is professor at the Politecnico di Milano, Italy.Irene Sabadini is professor at the Politecnico di Milano, Italy.

• - Part I Quaternionic functional analysis and related topics.- Functions of a Quaternionic Variable.- Quaternionic Banach and Hilbert Spaces.- Quaternionic Linear Operators on a Hilbert Space.- Reproducing Kernel Hilbert Spaces.- Part II Spaces of Slice Hyperholomorphic Functions.- Slice Hyperholomorphic Hardy Spaces.- de Branges Spaces.- Slice Hyperholomorphic Bergman Spaces.- Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces.- Slice Hyperholomorphic Fock Space.- Wiener Algebras.- Part III Various Extensions.- Slice Polyanalytic Functions.- Several Quaternionic Variables.- Function Spaces and Spectral Theories.