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 innerouter factorization theorem for the quaternionic Hardy space on the unit ball and we provide a characterization of quaternionic outer functions in terms of cyclicity
Monguzzi, A., Sarfatti, G. (2018). Shift invariant subspaces of slice L^2 functions. ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA, 43, 1045-1061 [10.5186/aasfm.2018.4366].
Shift invariant subspaces of slice L^2 functions
Monguzzi, A;
2018
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 innerouter 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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