Multiplication of closed balls in $\mathbb{C}^n$

Authors: PATRÍCIA DAMAS BEITES, ALEJANDRO PIÑERA NICOLÁS, JOSÉ DA SILVA LOURENÇO VITÓRIA

Abstract: Motivated by circular complex interval arithmetic, some operations on closed balls in $\mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $\mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n \in \{3, 7\}$, are studied. In addition, certain equations involving the defined multiplications are solved.

Keywords: Closed ball, multiplication, $2$-fold vector cross product, Hadamard product of vectors

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