loading page

Differentiable functions in a three-dimensional associative noncommutative algebra
  • Tetiana Kuzmenko,
  • Vitalii Shpakivskyi
Tetiana Kuzmenko
Zhytomyr Military Institute

Corresponding Author:[email protected]

Author Profile
Vitalii Shpakivskyi
Institute of Mathematics National Academy of Sciences of Ukraine
Author Profile


We consider a three-dimensional associative noncommutative algebra Ã2 over the field C, which contains the algebra of bicomplex numbers B(C) as a subalgebra. In this paper we consider functions of the form Φ(ζ)=f1123)I1+f2123)I2+f3123)ρ of the variable ζ=ξ1I12I23ρ, where ξ1, ξ2, ξ3 are independent complex variables and f1, f2, f3 are holomorphic functions of three complex variables. We construct in an explicit form all functions defined by equalities dΦ=dζ·Φ’(ζ) or dΦ=Φ’(ζ)·dζ. The obtained descriptions we apply to representation of the mentioned class of functions by series. Also we established integral representations of these functions.
23 Nov 2021Published in Advances in the Theory of Nonlinear Analysis and its Application. 10.31197/atnaa.912344