Hypercomplex Factorization of the Helmholtz Equation
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The main result of this paper is the construction of a global hypercomplex factorization of the Dirichiet problem for the Helmholtz equation. This result permits the reduction of the considered boundary value problem into two boundary value problems of first order for generalized analytic functions.
- Bauhaus University, Weimar Germany
fundamental solution, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, quaternionic algebra, eigenvalue problem, General topics in partial differential equations, Helmholtz equation, global factorization, Lyapunov boundary, Theoretical approximation in context of PDEs
fundamental solution, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, quaternionic algebra, eigenvalue problem, General topics in partial differential equations, Helmholtz equation, global factorization, Lyapunov boundary, Theoretical approximation in context of PDEs
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