Mathematical Sciences: Problems in Function Theory

本课题是函数论和算子论的数学研究。将进行三条线的调查。第一种方法涉及相对于封闭单位圆盘中所支持的某些类型的度量的多项式逼近。第二个领域涉及复n-空间中各种解析函数空间上的复合算子问题，包括复合算子的有界性、范数估计、紧性和谱性质等问题。最后，对n球的交换全纯自映射进行了研究。

This project is mathematical research in function theory and operator theory. Three lines of investigation will be pursued. The first involves polynomial approximation relative to certain kinds of measures supported in the closed unit disc. The second area involves problems concerning composition operators on various spaces of analytic functions in the disc and in the unit ball in complex n-space; this includes questions of boundedness and norm estimates, compactness, and spectral properties of composition operators. Finally, a study of commuting holomorphic self-maps of the n-ball will be initiated.