Let 𝔸 nm be an arbitrary n-dimensional commutative associative algebra over the field of
complex numbers with m idempotents. Let e 1= 1, e 2, e 3 be elements of 𝔸 nm which are …

Let $\mathbb {A} _n^ m $ be an arbitrary $ n $-dimensional commutative associative algebra
over the field of complex numbers with $ m $ idempotents. Let $ e_1= 1, e_2,\ldots, e_k …

In this paper, an analog of the conformable fractional derivative is defined in an arbitrary
finite-dimensional commutative associative algebra. Functions taking values in the indicated …

The idea of an algebraic-analytic approach to equations of mathematical physics means to
find a commutative Banach algebra such that monogenic functions with values in this …

In [2], a method for the formal construction of solutions of the three-dimensional Laplace
equation is developed by using power series in any harmonic algebra over the field of …

In this paper we introduce the φ A-differentiability for functions f: U⊂ R k→ R n, where U is
an open set, A is the linear space R n endowed with a unital associative commutative …

We obtain a constructive description of monogenic functions taking values in a finite-
dimensional commutative algebra with unit and radical of maximal dimensionality by means …

The methods involving the functions analytic in a complex plane for plane potential fields
inspire the search for the analogous efficient methods for solving the spatial and …

arXiv:1412.5142v1 [math.CV] 16 Dec 2014 Page 1 arXiv:1412.5142v1 [math.CV] 16 Dec 2014
УДК 517.548 ВСШпакiвський, ТСКузьменко Про один клас кватернiонних вiдображень …

In this paper we investigated some properties of holomorphic functions (belonging to the
kernel of the Dirac operator) defined on domains of the real Cayley-Dickson algebras. For …