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math.CV2025
An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra
S. A. Plaksa, V. S. Shpakivskyi, M. V. Tkachuk
We prove that a locally bounded and differentiable in the sense of Gateaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differen…
math.CV2024
Analog of Menchov-Trokhimchuk theorem for monogenic functions in subspace of the three-dimensional commutative algebra
M. V. Tkachuk
The aim of this work is to weaken the conditions of monogenity for functions that take values in subspaces of one concrete three-dimensional commutative algebras over the field of…
math.CV2012★ 1 cited
Integral geometry and Mizel's problem
Yu. B. Zelinskii, M. V. Tkachuk, B. A. Klishchuk
The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.