论文摘要
Bergman空间及其上的Toeplitz算子作为算子理论的一个活跃分支,不仅与众多数学分支有紧密联系,而且与其它学科也有不可分割的关联,特别是它们在小波分析和控制理论等学科中有着重要的应用.近十几年来,人们发现函数论和算子理论中的一些经典问题与Bergman空间及其Toeplitz算子密切相关,如:不变子空间问题. Bergman空间及Toeplitz算子的研究也引出了许多有趣的复分析和微分方程等问题.这使得Toeplitz算子研究一直持续升温.本文主要研究函数空间上具有无界符号的Toeplitz算子.第二章首先把Bergman空间上具有无界符号的Toeplitz算子推广到了单位多圆盘的情形.其次,把Bergman空间上以BMO为符号的Toeplitz算子情形推广到单位球上的情形.第三章把Dirichlet空间上具有无界符号的Toeplitz算子推广到加权的情形,且考虑了更为一般的Dirichlet空间上此类算子的情况.
论文目录
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