紧复流形上的星算子定义及伴随算子
The Definition of Star Operator and Some Adjoint Operators on Compact Complex Manifold

本文仿照Morrow-Kodaira版本的紧复流形上的星算子定义，结合Griffiths-Harris版本的星算子，从定理的观点再引出星算子定义。通过这种方式，一方面可以揭示星算子局部表达式中附带的一些复杂系数如2^p+q、(-1)^C_n2+np、(√-1/2)ⁿ的本源及趣味之美，另一方面可以清晰地看到经典的两种星算子存在的微妙差异，并引发全纯算子、反全纯算子在(p,q)型形式空间Γ(A^p,q(M))的整体Hermite内积之下的伴随算子的细微差别。
In this paper, following the definition of star operator on complex compact manifold from Mor-row-Kodaira version, and combining with the Griffiths-Harris version of star operator, we give again the definition of star operator from the theorem view point. Via this mean, on one hand, we can reveal the original and interesting beauty of some complicated coefficients attached to the local expression of star operator, such as 2^p+q, (-1)^C_n2+np, (√-1/2)ⁿ; on the other hand, it is clear to see that there are some delicate differences between two classical definitions of star operator. Furthermore, it causes that there are subtle differences between adjoint operators corresponding the holomorphic operator and anti-holomorphic operator on the space Γ(A^p,q(M)) by (p,q) type differential forms under the global Hermitian inner product.