Multi Mq-monogenic function in different dimension

A metamonogenic of first-order function or simply metamonogenic function is a function that satisfies the differential equation (D - λ)u = 0, where D is the Cauchy-Riemann operator and λ can be real or Cliffordvalued constant (see [4]). Using this definition we can say that a multimetamonogenic function u is separately metamonogenic in several variables x^(j), j = 1, ⋯, n with n ≥ 2, if x^(j) = (x^(j)₁, ⋯, x^(j)_mj) runs in the Euclidean space ℝ^mj and (D_j - λ)u = 0, for each j = 1, ⋯, n, where D_j is the corresponding Cauchy-Riemann operator in the space ℝ^mj. Using the theory of algebras of Clifford type depending on parameters (see [11, 12]), the present proposal discusses the properties of u in case the dimensions m_j are different from each other for multi Mq-monogenic functions, following the ideas exhibited in [9, 10].