Shift invariant subspaces of slice L^2 functions
Copyright policy )Shift invariant subspaces of slice L^2 functions
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
- University of Florence Italy
- University of Bergamo Italy
- University of Milan Italy
Hardy spaces, Mathematics - Complex Variables, Inner functions of one complex variable, inner-outer factorization, functions of a quaternionic variable, Functions of hypercomplex variables and generalized variables, Functions of a quaternionic variable, invariant subspaces, inner-outer factorization, FOS: Mathematics, functions of a quaternionic variable; invariant subspaces; inner-outer factorization, Complex Variables (math.CV), invariant subspaces, Functions of a quaternionic variable; inner-outer factorization; invariant subspaces;
Hardy spaces, Mathematics - Complex Variables, Inner functions of one complex variable, inner-outer factorization, functions of a quaternionic variable, Functions of hypercomplex variables and generalized variables, Functions of a quaternionic variable, invariant subspaces, inner-outer factorization, FOS: Mathematics, functions of a quaternionic variable; invariant subspaces; inner-outer factorization, Complex Variables (math.CV), invariant subspaces, Functions of a quaternionic variable; inner-outer factorization; invariant subspaces;
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