Quaternion $H$-type group and differential operator $Δ_λ$

Details Quaternion $H$-type group and differential operator $Δ_λ$ Quaternion $H$-type group and differential operator $Δ_λ$

2006-10-02

arxiv.org/abs/math/0610074v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

We study the relations between the quaternion $H$-type group and the boundary of the unit ball on two dimensional quaternionic space. The orthogonal projection of the space of square integrable functions defined on quaternion $H$-type group into its subspace of boundary values of $q$-holomorphic functions is consider. The precise form of Cauchy-Szego kernel and the orthogonal projection operator is obtained. The fundamental solution for the operator $\Delta_{\lambda}$ is found.

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