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Multi Mq-monogenic function in different dimension

Abstract:

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 ℝmj and (Dj - λ)u = 0, for each j = 1, ⋯, n, where Dj is the corresponding Cauchy-Riemann operator in the space ℝmj. 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 mj are different from each other for multi Mq-monogenic functions, following the ideas exhibited in [9, 10].