An extension theorem for slice monogenic functions and some of its consequences

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Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, unknown): “For the generalization to functions with values in a Clifford algebra, called again slice hyperholomorphic or slice monogenic functions, we refer the reader to [44, 46, 45], and to [57] for functions with values in a real alternative algebra.”
Slice regular functions on real alternative algebras (2010, background): “See also [9] for a similar result about slice monogenic functions.”
On Two Approaches to the Bergman Theory for Slice Regular Functions (2013, background): “More in general, by slice hyperholomorphic functions we mean both slice regular functions and slice monogenic functions which are the monogenic version of the theory of slice regular functions, see [6, 8, 10, 11].”
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “Slice hyperholomorphic functions have two main formulations according to the fact that the functions we consider are defined on quaternions and are quaternion-valued, in this case the functions are called slice regular, see [32, 15, 19] or the functions are defined on the Euclidean space R and have ”
Entire slice regular functions (2015, methodology): “The theory was developed also for functions with values in a Clifford algebra, see [72], [73], for functions with values in a real alternative algebra, see [117].”