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

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DOI: 10.4236/apm.2012.22013    6,651 Downloads   12,480 Views Citations

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.

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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.

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