Quasi-conformal functions of quaternion and octonion variables, their integral transformations

Abstract

The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their residues and argument principle are studied. It is proved, that the family of all quasi-conformal diffeomorphisms of a domain form a topological group relative to composition of mappings. Cases when it is a finite-dimensional Lie group over $\mathbf{R}$ are studied. Relations between quasi-conformal functions and integral transformations of functions over quaternions and octonions are established. For this, in particular, noncommutative analogs of the Laplace and Mellin transformations are studied and used. Examples of such functions are given. Applications to problems of complex analysis are demonstrated.

34 references, 41 pages

References in corpus (1)

• Functions of several Cayley-Dickson variables and manifolds over them

Cited by in corpus (5)

• Manifolds over Cayley-Dickson algebras and their immersions
• Affine and wrap algebras over octonions
• Line integration and second order partial differential equations over Cayley-Dickson algebras
• Schauder bases in Dirac modules over quaternions
• Residues of functions of Cayley-Dickson variables and Fermat's last theorem