abstract 73

Bulletin of Computational Applied Mathematics (Bull CompAMa)

73

The fundamental solution for the anisotropic Helmholtz operator in the algebra of complex quaternions

Damian Cedeño López, Carmen Vanegas Espinoza, Franklin Vargas Jiménez

In the present work we study the anisotropic Helmholtz operator $\tilde{\Delta} + \lambda^2$, where $\tilde{\Delta} = div(B\nabla)$ and $B\in{\mathbb{R}}^{3\times 3}$ is a symmetric and positive definite matrix. For this operator we show a fundamental solution under the framework of the complex quaternions algebra $\mathbb{H}(\mathbb{C})$. This allows us to find a Cauchy-Pompeiu type integral formula and solve the non-homogeneous equation associated with this operator.

Keywords: Anisotropic Helmholtz operators; fundamental solution; complex quaternions.

Cite this paper:

Cedeño D., Vanegas C.J., Vargas F.

Anisotropic Helmholtz operator in the algebra of complex quaternions

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 10, No.1, pp.109-123, 2022.