数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 203-214.doi: 10.1016/S0252-9602(15)30088-6

• 论文 • 上一篇    下一篇

SZEGÖ KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

贺福利1, 库敏2, Uwe KÄHLER2   

  1. 1. School of Mathematics and Statistics, Central South University, Changsha 410083, China;
    2. CIDMA, Department of Mathematics, University of Aveiro, Portugal
  • 收稿日期:2014-10-06 修回日期:2015-03-12 出版日期:2016-01-30 发布日期:2016-01-30
  • 通讯作者: Min KU,E-mail:kumin0844@163.com E-mail:kumin0844@163.com
  • 作者简介:Fuli HE,E-mail:hefuli999@163.com;Uwe KÄHLER,E-mail:ukaehler@ua.pt
  • 基金资助:

    The project is supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology(FCT——Funda\c{c

SZEGÖ KERNEL FOR HARDY SPACE OF MATRIX FUNCTIONS

Fuli HE1, Min KU2, Uwe KÄHLER2   

  1. 1. School of Mathematics and Statistics, Central South University, Changsha 410083, China;
    2. CIDMA, Department of Mathematics, University of Aveiro, Portugal
  • Received:2014-10-06 Revised:2015-03-12 Online:2016-01-30 Published:2016-01-30
  • Contact: Min KU,E-mail:kumin0844@163.com E-mail:kumin0844@163.com
  • Supported by:

    The project is supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology(FCT——Funda\c{c

摘要:

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.

关键词: Hardy space, Hermitean Clifford analysis, Szegö, projection, matrix function

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

中图分类号: 

  • 30G35