具有可变算子值结构常数的代数及其应用
Algebras with Variable Operator-Valued Structural Constants and Their Applications
- Institute of Mathematics of the NAS of Ukraine（乌克兰国家科学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文引入具有可变算子值结构常数的代数，发展其中单演函数理论，建立相容性条件，证明分量满足变系数二阶算子微分方程，为多种微分方程提供构造性求解方法。
AI中文摘要：
我们引入了一类具有可变算子值结构常数的新代数，并在这类代数中发展了单演函数理论的要素。建立了结构算子的相容性条件。证明了单演函数的分量满足具有变系数的二阶算子微分方程，并证明了逆命题。所提出的方法为获得各种微分、积分-微分和泛函-微分方程的解提供了一种构造性方法。文中给出了几个说明性例子。
英文摘要：
We introduce a new class of algebras with variable operator-valued structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural operators are established. It is shown that the components of monogenic functions satisfy second-order operator-differential equations with variable coefficients, and converse results are proved. The proposed approach provides a constructive method for obtaining solutions of various differential, integro-differential, and functional-differential equations. Several illustrative examples are presented.
