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arXiv · 1802.02344

Shift invariant subspaces of slice $L^2$ functions

Alessandro Monguzzi·Giulia Sarfatti
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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.

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Alessandro Monguzzi, Giulia Sarfatti. 2018-02-07. Shift invariant subspaces of slice $L^2$ functions. https://arxiv.org/abs/1802.02344

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