  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.

Complex Variables