Foundations of the Theory of G-monogenic Mappings in Noncommutative Algebras

This monograph develops a comprehensive theory of G‑monogenic mappings in noncommutative algebras, combining algebraic structure with analytic techniques. Building on quaternionic and hypercomplex analysis, the authors introduce new classes of G‑ and H‑monogenic mappings, establish their fundamental properties, and provide explicit constructive representations via holomorphic functions. Classical tools of complex analysis—including the Cauchy integral theorem, Morera’s theorem, and Taylor and Laurent expansions—are extended to noncommutative settings. The theory is further connected to elliptic partial differential equations, demonstrating explicit solution methods. The book offers a unified framework in hypercomplex analysis, noncommutative algebra, and applied complex analysis, making it a suitable reference for researchers working in these fields.