Plenary Talk


Regular quaternionic functions and their applications


Yuri Grigor'ev
Nord-Eastern Federal University, Russian Federation

Abstract

The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given.



ISSN 1611 - 4086 | © IKM 2015