C^(N)上Fock空间上的有限余维加权复合算子

Finite Co-dimensional Weighted Composition Operators on the Fock Space over C^(N)

本文给出了C^(N)上Fock空间上有限余维加权复合算子的完全刻画,该刻画与Fock空间上循环向量的刻画密切相关.主要结论表明,Fock空间上一个有界加权复合算子是有限余维的当且仅当其复合符号是1次可逆解析多项式,且当N=1时,其加权符号至多有有限个零点;当N≥2时,其加权符号没有零点.

In this paper,finite co-dimensional weighted composition operators on the Fock space over C^(N)are characterized completely,which is closely related to the characterization of cyclic vectors in the Fock space.The main result shows that a bounded weighted composition operator on the Fock space is finite co-dimensional if and only if the composite symbol is an invertible analytic polynomial with degree 1 and the weighted symbol has at most finite zeros when N=1 or is nonvanishing when N≥2.