Open AccessQuaternionic methods in integral transforms of geophysical interest
Author(s) -
Davies A. J.,
Foot R.,
Joshi G. C.,
McKellar B. H. J.
Publication year - 1989
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1989.tb02042.x
Subject(s) - cauchy distribution , cauchy's integral formula , integral transform , mathematics , quaternion , mathematical analysis , cauchy's integral theorem , pure mathematics , cauchy problem , initial value problem , geometry
SUMMARY It is well known that the Cauchy integral formula may be used in the study of integral transforms, leading to an elegant formulation in 2‐D. We show that the quaternionic analysis of Fueter, and in particular the quaternionic analogue of the Cauchy formula, may be applied to derive integral transforms of vector functions in 3‐D in an elegant manner. In particular we show that this result contains as special cases results of interest in the study of integral transforms in geophysics.