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Multidimensional Laplace Transforms over Quaternions, Octonions and Cayley-Dickson Algebras, Their Applications to PDE
Department of Applied Mathematics, Moscow State Technical University, MIREA, Moscow, Russia
- 1 Department of Applied Mathematics, Moscow State Technical University, MIREA, Moscow, Russia
Advances in Pure Mathematics·Volume 02 (2012)·Pages 63–103·Published 22 March 2012·DOI10.4236/apm.2012.22013
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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.
KeywordsLaplace TransformQuaternion Skew FieldOctonion AlgebraCayley-Dickson AlgebraPartial Differential EquationNon-Commutative Integration
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