Constructive description of monogenic functions in a finite-dimensional commutative associative algebra
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Vitalii Shpakivskyi
Abstract
Let š¯”ønm be an arbitrary n-dimensional commutative associative algebra over the field of complex numbers with m idempotents. Let e1 = 1, e2, e3 be elements of š¯”ønm which are linearly independent over the field of real numbers. We consider monogenic (i.e., continuous and differentiable in the sense of Gateaux) functions of the variable xe1 + ye2 + ze3, where x, y, z are real, and obtain a constructive description of all mentioned functions by means of holomorphic functions of complex variables. It follows from this description that monogenic functions have Gateaux derivatives of all orders.
The author expresses a gratitude to Professor S. A. Plaksa and Mr. R. P. Pukhtaievych for numerous discussions and valuable advices.
Ā© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order
- Segalā€“Bargmann transform and Paleyā€“Wiener theorems on Heisenberg motion groups
- Solution and fuzzy stability of a mixed type functional equation
- Harmonic analysis and generalized functional equations for the cosine
- Lipschitz conditions for the generalized Fourier transform associated with the Jacobiā€“Cherednik operator on ā„¯
- Constructive description of monogenic functions in a finite-dimensional commutative associative algebra
Articles in the same Issue
- Frontmatter
- Stability and boundedness of solutions of a certain n-dimensional nonlinear delay differential system of third-order
- Segalā€“Bargmann transform and Paleyā€“Wiener theorems on Heisenberg motion groups
- Solution and fuzzy stability of a mixed type functional equation
- Harmonic analysis and generalized functional equations for the cosine
- Lipschitz conditions for the generalized Fourier transform associated with the Jacobiā€“Cherednik operator on ā„¯
- Constructive description of monogenic functions in a finite-dimensional commutative associative algebra
