Abstract
We consider several questions related to the removability of singularities for regular functions of quaternionic variables. In particular we use an old idea of Severi to prove that a function f : ℍ × ℝ → ℍ regular in the first variable and real analytic in the second variable, cannot have compact singularities; we show how this result must be modified in the case of functions defined on biquaternions. Finally, we construct a class of regular functions on ℍ2 for which we can remove singularities such as K × ℝ3 with K compact in ℝ5.
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Napoletani, D., Sabadini, I., Struppa, D.C. (2000). Variations on a theorem of Severi. In: de Arellano, E.R., Vasilevski, N.L., Shapiro, M., Tovar, L.M. (eds) Complex Analysis and Related Topics. Operator Theory Advances and Applications, vol 114. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8698-7_14
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DOI: https://doi.org/10.1007/978-3-0348-8698-7_14
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9734-1
Online ISBN: 978-3-0348-8698-7
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