Arithmetic for closed balls

Abstract

Inspired by circular complex interval arithmetic, an arithmetic for closed balls in Rⁿ is pursued. In this sense, the properties of certain operations on closed balls in Rⁿ, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n є {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R², are extended to closed balls in Rⁿ.