Author(s)

Sergey Victor Ludkovsky

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

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.

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

S. Ludkovsky, "Multidimensional Laplace Transforms over Quaternions, Octonions and Cayley-Dickson Algebras, Their Applications to PDE," Advances in Pure Mathematics, Vol. 2 No. 2, 2012, pp. 63-103. doi: 10.4236/apm.2012.22013.