具有可变结构常数的代数及其应用
Algebras with Variable Structural Constants and Their Applications
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中文总结 AI 辅助
本文引入具有可变结构常数的代数，建立单演函数理论，证明其分量满足变系数二阶偏微分方程，并提供构造显式解的方法。
中文摘要 AI 辅助
我们引入了一类具有可变结构常数的新代数，并发展了此类代数中单演函数理论的基本要素。建立了结构函数的相容性条件。证明了单演函数的分量满足某些具有变系数的二阶偏微分方程，并证明了逆命题。该方法为获得此类方程的显式解提供了一种构造性途径。文中给出了若干示例。
英文摘要
We introduce a new class of algebras with variable structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural functions are established. It is shown that the components of monogenic functions satisfy certain second-order partial differential equations with variable coefficients, and converse results are proved. This approach provides a constructive method for obtaining explicit solutions of such equations. Several illustrative examples are presented.
发表机构
- Institute of Mathematics of the NAS of Ukraine（乌克兰国家科学院数学研究所）
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