arXiv math/06100742006-10-02math.APmath.CVmath.DG

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

Der-Chen Chang, Irina Markina

备注：: 18 pages

英文摘要：

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 $Δ_λ$ is found.

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