An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra
Complex Variables
2025-02-14 v1 Analysis of PDEs
Abstract
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 differentiable in the sense of Lorch.
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Cite
@article{arxiv.2502.08809,
title = {An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra},
author = {S. A. Plaksa and V. S. Shpakivskyi and M. V. Tkachuk},
journal= {arXiv preprint arXiv:2502.08809},
year = {2025}
}
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15 pages