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

Sergey Victor Ludkovsky

Department of Applied Mathematics, Moscow State Technical University, MIREA, Moscow, Russia.

DOI: 10.4236/apm.2012.22013                

Abstract

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.

Keywords

Laplace Transform; Quaternion Skew Field; Octonion Algebra; Cayley-Dickson Algebra; Partial Differential Equation; Non-Commutative Integration

Conflicts of Interest

The authors declare no conflicts of interest.

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