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Entradas recentes
On the growth type of entire solutions to higher dimensional polynomial Cauchy-Riemann equations
2018 - Almeida, Regina De; Krausshar, R.S.; Almeida, Regina De
In this paper we study same basic properties of growth types for solutions to polynomial Cauchy-Riemann equations.
Wiman-Valiron theory for higher dimensional polynomial Cauchy-Riemann equations
2018 - Almeida, Regina De; Krausshar, R.S.; Almeida, Regina De
In this paper, we introduce different kinds of growth orders for the set of entire solutions to the most general framework of higher-dimensional polynomial Cauchy-Riemann equations
Π_{ i=1}^p ( − 𝜆_i)^{k_i} f = 0, where ∶= 𝜕f /𝜕x_0 + Σ_{i=1}^n e_i 𝜕f/𝜕x_i
is the hypercomplex Cauchy-Riemann operator, 𝜆i are arbitrarily chosen nonzero complex constants, and ki are arbitrarily chosen positive integers. The core ingredient is a projection formula that establishes a relation to the ki-monogenic component functions, which are null-solutions to iterates of the Cauchy-Riemann operator that we studied in earlier works. Furthermore, we briefly outline the analogies of the Lindelöf-Pringsheim theorem in this context
Elliptic Biquaternionic sequence with vietoris’ numbers as Its components
2024 - Almeida, Regina De; Catarino, Paula; Almeida, Regina De
In this study, we introduce an elliptic biquaternionic sequence with Vietoris’ numbers as its components and discuss some of its properties. Also, the generating function and some identities in terms of elliptic biquaternionic sequence with Vietoris’ numbers are given. Furthermore, the construction of this elliptic biquaternion sequence is presented using matrices that generate the quaternionic sequence where the components are Vietoris’ number, and also by applying the determinant to a special kind of matrices.