Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

Abstract

ABSTRACT. The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

Alternative to the Hypercomplex Fourier Transform Definition

“…In order to generalize the Fourier transform to its quaternionic form, first we described Fourier series and we introduced the hypercomplex model by considering results from [8,9], which unable to obtain a formulation for hypercomplex Fourier transform, which depends on a product internal. Furthermore, since not few models of Theoretical Physics may be analyzed through the geometry and algebra of hypercomplex, it will be our concern to concentrate the next steps in making all possible applications of our results in the context of unified physical theories for higher dimensional space-times.…”