SZEG? KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg? 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 Szeg? projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szeg? projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szeg? kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.