Tolstov`s Theorem in the Commutative Banach Algebra A3
M.V. Tkachuk
TL;DR
This paper explores weakened conditions for monogenic functions in a three-dimensional commutative algebra over complex numbers, focusing on continuity and Gâteaux differentiability.
Contribution
It extends the theory of monogenic functions by relaxing the usual conditions in a specific algebraic setting.
Findings
Conditions for monogenicity are weakened in the algebra A3.
The paper characterizes functions with Gâteaux derivatives in this context.
Results generalize classical theorems to a broader class of functions.
Abstract
In this paper, the conditions of monogenicity are weakened for functions with values in a three-dimensional commutative algebra over the field of complex numbers. By monogenicity we mean continuity and the existence of the G\^ateaux derivative.
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