Quaternionic Hardy spaces in the open unit ball and half space and Blaschke products

30th International Colloquium on Group Theoretical Methods in Physics

Alpay, Daniel^1 ; Colombo, Fabrizio^2 ; Sabadini, Irene^2

Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva

84105, Israel^1

Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, Milano

20133, Italy^2

关键词: Blaschke product;    Half spaces;    Hardy space;    Positive real;    Unit ball;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012009/pdf
DOI  :  10.1088/1742-6596/597/1/012009

来源: IOP

【 摘 要 】

The Hardy spaces H2(B) and H2(H+), where B and H+denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.