Multidimensional Laplace transforms over Cayley-Dickson algebras and partial differential equations

Details Multidimensional Laplace transforms over Cayley-Dickson algebras and partial differential equations Multidimensional Laplace transforms over Cayley-Dickson algebras and partial differential equations

2010-04-25

arxiv.org/abs/1004.4355v1

Mathematics

Complex Variables

66 pages

Scientific paper

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.

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