Abstract
The Fueter mapping theorem in integral form introduced in [86], see Chapter 2.2, provides an integral transform that turns slice hyperholomorphic functions into Fueter regular ones. By formally replacing the scalar variable in this integral transform by an operator T, we obtain a functional calculus for Fueter regular functions that is based on the theory of slice hyperholomorphic functions. The F-functional calculus was introduced and studied in the following papers [54, 78, 81, 86].
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Colombo, F., Gantner, J., Kimsey, D.P. (2018). The F-Functional Calculus for Bounded Operators. In: Spectral Theory on the S-Spectrum for Quaternionic Operators. Operator Theory: Advances and Applications, vol 270. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-03074-2_7
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DOI: https://doi.org/10.1007/978-3-030-03074-2_7
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