Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions

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Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “The book [27] collects some of the main results on the theory of slice hyperholomorphic functions and the related functional calculi.”
A nonconstant coefficients differential operator associated to slice monogenic functions (2012, background): “In the past few years, the theory of slice monogenic functions has had a rapid development mainly stimulated by the application to a very elegant functional calculus for not necessarily commuting operators, either bounded or unbounded; see [2, 4, 7, 8, 9] and the recent monograph [10].”
The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum (2014, unknown): “6 in [17] that σS(ZT ) ⊆ {p ∈ H : p ≤ ‖ZT‖} and hence we have that σS(ZT ) ∩ Cj ⊆ B.”
A New Resolvent Equation for the $$S$$S-Functional Calculus (2013, unknown): “For more details on the S-functional calculus and the function theory on which it is based see the the monograph [19].”
The C-property for slice regular functions and applications to the Bergman space (2013, background): “After their definition in [15] which has been generalized to the case of functions with values in a Clifford algebra in [8], these functions have been intensively studied during the past years and their theory, as well as the application to the functional calculus, is treated in the book [9].”