By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded s...By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.展开更多
基金supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT–Fundao para a Ciência e a Tecnologia)within project UID/MAT/04106/2013the recipient of a Postdoctoral Foundation from FCT under Grant No. SFRH/BPD/74581/2010
文摘By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.
