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

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

2007-03-27

arxiv.org/abs/math/0703788v1

Far East Journal of Mathematical Sciences (FJMS) 2008

Mathematics

Complex Variables

34 references, 41 pages

Scientific paper

08.4194/S449-453

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 $\bf R$ 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.

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