We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic space.The orthogonal projection of the space of square integrable functions defined on q...We study the relations between the quaternion H-type group and the boundary of the unit ball on the 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 considered.The precise form of Cauchy-Szeg(?)kernel and the orthogonal projection operator is obtained.The fundamental solution for the operatorΔ_λis found.展开更多
基金The first author is partially supported by a Competitive Research Grant at Georgetown University(Grant No.GD2236120)The second author is partially supported by grants of the Norwegian Council(Grant Nos.177355/V30,180275/D15)by the grant of the European Science Foundation Networking Programme HCAA.
文摘We study the relations between the quaternion H-type group and the boundary of the unit ball on the 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 considered.The precise form of Cauchy-Szeg(?)kernel and the orthogonal projection operator is obtained.The fundamental solution for the operatorΔ_λis found.
