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

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

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Frontiers in Mathematics

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

Tetiana S. Kuzmenko | Vitalii S. Shpakivskyi

Mathematics / Complex Analysis

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.

 

Tetiana S. Kuzmenko is an associate professor of the Department of Fundamental Sciences at the Zhytomyr Military Institute. She received her Ph.D. in mathematics from the Institute of Mathematics of the National Academy of Sciences of Ukraine in 2018. Her research focuses on hypercomplex analysis and the theory of monogenic mappings in noncommutative algebras. Her work combines methods of complex analysis with quaternionic and bicomplex structures, with applications to partial differential equations and analytic function theory.

Vitalii S. Shpakivskyi is a leading research fellow of the Department of Complex Analysis and Potential Theory at the Institute of Mathematics of the National Academy of Sciences of Ukraine. He received his Ph.D. in mathematics from the Institute of Mathematics of the National Academy of Sciences of Ukraine in 2011. He began his academic and research career at the Zhytomyr State University. He is the recipient of many research grants and awards including Ukraine’s Parliament Prize for young scientists in 2013 and the Ukrainian President Prize for young scientists in 2022. An author of more than 80 research articles, his research interests include complex and hypercomplex analysis, analytic function theory of complex variables and monogenic function theory in Banach algebras.


Publication Date: 07 September 2026
Publisher: Springer Nature Switzerland
Imprint: Birkhäuser
ISBN-13: 9783032330994
Format: Paperback / softback

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