SOME SPECTRAL PROPERTIES OF REPRESENTATIONS OF HYPERCOMPLEX WAVE FIELDS

Abstract

In previous articles we have discussed the representation of 4-dimensional wave fields in terms of a commutative hypercomplex system over the field of real numbers. With division and nontransitive equality. In the present paper we discuss the spectral and other structural properties of this representation. We note in conclusion that a conformal homomorphism enables us to deparallelize fully all operations, which is consistent in a natural way with the architecture of two-processor systems, so that the time needed for calculation of four-dimensional geophysical models is essentially the same as for the analogous planar models.