S.V. Lüdkovsky and F. van Oystaeyen, “Differentiable Functions of Quaternion Variables,” Bulletin des Sciences Mathématiques, Vol. 127, No. 9, 2003, pp. 755-796. doi:10.1016/S0007-4497(03)00063-0

has been cited by the following article:

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

  AUTHORS: Sergey Victor Ludkovsky

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

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.2, March 22, 2012

  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.