LINEARIZATION OF LAPLACIAN OF A HYPERHOLOMORPHIC FUNCTION OF EIGHT REAL VARIABLES

Abstract

When defining a hyperholomorphic function by defining a number system asnon-commutative base for products, the proposed differential operator is investigated, and differences with variables in the existing number system are discovered in Octonions. We define algebraic properties and operations for elements of Cayley algebra called octonionand we give a function using octonion as a variable. We propose a corresponding differential operator and Investigate that the defined differential operator is the linearization of Laplacianon real multivariate. By defining the hyperholomorphic function of the octonion variable,the utilization and properties of differential operators are investigated.