Abstract
In this paper, we compile a variety of results on the \(\lambda -\)Laplacian operator, denoted by \(\varDelta _{\lambda }\), a generalization of the well-known Laplacian in \({\mathbb {R}^n}\). We have compiled a list of known properties for \(\varDelta _{\lambda }\) when \(\lambda = \frac{n-2}{2}\) and present analogous properties for \(\varDelta _{\lambda }\). We close by discussing the \(\lambda -\)Poisson kernel, the function that solves the Dirichlet problem on the closed ball in \({\mathbb {R}^n}\).
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Ballenger-Fazzone, K., Nolder, C.A. (2018). Lambda-Harmonic Functions: An Expository Account. In: Cerejeiras, P., Nolder, C., Ryan, J., Vanegas Espinoza, C. (eds) Clifford Analysis and Related Topics. CART 2014. Springer Proceedings in Mathematics & Statistics, vol 260. Springer, Cham. https://doi.org/10.1007/978-3-030-00049-3_1
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