Abstract
The aim of this work is to show that the operator G, which has been introduced in Colombo et al. (Trans Am Math Soc 365:303–318, 2013) and whose kernel kerG coincides with the set of quaternionic slice regular functions, is a member of a family of operators with similar properties, such that all the members possess the respective versions of Stokes and Cauchy–type integral theorems. As direct consequences, these theorems are obtained for slice regular functions.
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Communicated by Irene Sabadini.
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The author was partially supported by CONACYT and thanks to Professor Michael Shapiro for his help and support.
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Cervantes, J.O.G. On Cauchy Integral Theorem for Quaternionic Slice Regular Functions. Complex Anal. Oper. Theory 13, 2527–2539 (2019). https://doi.org/10.1007/s11785-019-00913-2
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DOI: https://doi.org/10.1007/s11785-019-00913-2
Keywords
- Quaternions
- Non-constant coefficient differential operator
- Quaternionic Stokes theorem
- Quaternionic Cauchy integral theorem
- Quaternionic slice regular functions