Multidimensional Laplace Transforms over Quaternions, Octonions and Cayley-Dickson Algebras, Their Applications to PDE

• 作者: Sergey Victor Ludkovsky
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Laplace Transform Quaternion Skew Field OCTONION ALGEBRA Cayley-Dickson ALGEBRA Partial Differential Equation NON-COMMUTATIVE Integration
• 年，卷（期）: 2012,（2）
• 页码范围: 63-103
• 页数: 41页
• 分类号: O1

摘要

Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. Applications to partial differential equations including that of elliptic, parabolic and hyperbolic type are investigated. Moreover, partial differential equations of higher order with real and complex coefficients and with variable coefficients with or without boundary conditions are considered.