Minkowski geometric algebra of complex sets
type: Item
instance of: scholarly article
title: Minkowski geometric algebra of complex sets
zbMATH Open document ID: 0987.51012
DOI: 10.1023/A:1010318011860
author: Rida T. Farouki
author: Bahram Ravani
author: Hwan Pyo Moon
published in: Geometriae Dedicata
publication date: 2002-06-16T00:00:00Z
review text: For subsets \(A\) and \(B\) of the field of complex numbers two operations are defined, the sum of \(A\) and \(B\) as \(\{a+b : a\in A\), \(b\in B\}\), and their product (by replacing + with \(\times\) in the definition). The sum has been introduced by H. Minkowski in 1903 and studied extensively. The authors devote this paper to the study of the product operation, in particular to the effect multiplication by lines and circles has on various curves. The motivation behind this study lies in the potential applications to ``a generalization of real interval arithmetic to the complex domain, reflection and refraction of wavefronts in geometrical optics, stability characterization of multi-parameter control systems,'' mathematical morphology, and in the expectation that many more such applications will be found.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 51M15
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65G40
zbMATH DE Number: 1658569
zbMATH Keywords: Minkowski geometric algebra
zbMATH Keywords: complex sets
MaRDI profile type: Publication
full work available at URL: a:1010318011860
OpenAlex ID: W2108951449
description: scientific article; zbMATH DE number 1658569