SZEGÖ KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

doi:10.1016/S0252-9602(15)30088-6

Abstract

Abstract:

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

Key words: Hardy space, Hermitean Clifford analysis, Szegö, projection, matrix function

CLC Number:

30G35

Fuli HE, Min KU, Uwe KÄHLER. SZEGÖ KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS[J].Acta mathematica scientia,Series B, 2016, 36(1): 203-214.

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