Hardy空间上复合算子的伴随表示

Representation of the Adjoint of Composition Operator on Hardy Space

Hardy空间上的复合算子的伴随算子具有很好的性质,但对一般情形而言,一直没有关于它的明确表达式．Cowen于1988年给出了(?)为D上的线性分式自映射情形时C*(?)的表达式,并且于2000年给出了n个变量情形的推广．他指出,正是由于没有一般情形的C*(?)的表达式,在很大程度上,阻碍了复合算子理论的发展．该文给出了Hardy空间上的复合算子伴随的准确表达式．

The adjoint operators of composition operators on Hardy space have nice properties. But in general, the exact representation has not been known. In 1988 Cowen got a representation of C^＊φ when φ is linear fraction transformation in D. In 2000, he generalized the result to the case of n variables. He pointed out that one of the main difficulties in advancing a general theory of composition operators is that a nice representation of C^＊φ is unknown. In this paper, the author gives exact representation of the adjoint of composition operator on Hardy space.