Shift invariant subspaces of slice $L^2$ functions

Alessandro Monguzzi; Giulia Sarfatti

paper

Shift invariant subspaces of slice $L^{2}$ functions

arXiv:1802.02344

Abstract

In this paper we characterize the closed invariant subspaces for the ( $*$ -)multiplier operator of the quaternionic space of slice $L^{2}$ functions. As a consequence, we obtain the inner-outer factorization theorem for the quaternionic Hardy space on the unit ball and we provide a characterization of quaternionic outer functions in terms of cyclicity.

19 pages. Typos fixed and minor changes

Shift invariant subspaces of slice L2 functions

Abstract

Shift invariant subspaces of slice $L^{2}$ functions