Functions of several Cayley-Dickson variables and manifolds over them

Abstract

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde{\partial }$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated.

References in corpus (2)

• Zeros of polynomials over Cayley-Dickson algebras
• Differentiable functions of Cayley-Dickson numbers

Cited by in corpus (14)

• Quasi-conformal functions of quaternion and octonion variables, their integral transformations
• Manifolds over Cayley-Dickson algebras and their immersions
• Metagroups and their smashed twisted wreath products
• Affine and wrap algebras over octonions
• Line integration and second order partial differential equations over Cayley-Dickson algebras
• Wrap groups of fiber bundles over quaternions and octonions
• Left invariant measures on locally compact fan loops
• Octonion random functions and integration of stochastic PDEs
• Homotopism of homological complexes over nonassociative algebras with metagroup relations
• Multidimensional Laplace transforms over Cayley-Dickson algebras and partial differential equations
• Schauder bases in Dirac modules over quaternions
• On structure of topological metagroups
• Analytic extensions of functions of Cayley-Dickson variables
• Separability of metagroup algebras