On differentiable and monogenic functions in a harmonic algebra

Authors

  • S. A. Plaksa Institute of Mathematics of the National Academy of Sciences of Ukraine

Abstract

For locally bounded and differentiable in the sense of G\^ateaux functions Φ given in a three-dimensional commutativeharmonic algebra with two-dimensional radical, we prove the following statement: if the function Φ domain is convex "in the radical direction" and the difference ζ1ζ2 belongs to the radical, the difference Φ(ζ1)Φ(ζ2) belongs also to the radical. As a result, we prove that locally bounded and differentiable in the sense of G\^ateaux functions are also differentiable in the sense of Lorch.

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Published

2017-04-25

How to Cite

Plaksa, S. A. (2017). On differentiable and monogenic functions in a harmonic algebra. Transactions of Institute of Mathematics, the NAS of Ukraine, 14(1), 210–221. Retrieved from https://trim.imath.kiev.ua/index.php/trim/article/view/114