加权Fock空间F_α~2上的测不准原理的推广（英文）

FURTHER DISCUSSION ON UNCERTAINTY PRINCIPLES FOR THE α-FOCK SPACE F_α~2

对α> 0,本文主要研究了复平面上的加权Fock空间F_α~2上的自伴算子和线性算子的测不准原理.利用泛函分析中的一般性原理,在F_α~2上构造了两个线性算子Tf=(f′)/α和T*=zf.进一步,构造了满足条件的两个自伴算子A和B,使得[A,B]为恒等算子的常数倍,得到了F_α~2上更精确的算子的测不准原理形式,其中T*是T的对偶算子,[A,B]=AB-BA为A和B的换位置.本文的结果推广并完善了屈非非和朱克和在文献[1]和[2]中的结果.

In this article,forα>0,we characterize several versions uncertainty principles of self-adjoint operators and linear operators for theα-fock space Fα^2 in the complex plane.By using the general result from functional analysis,we find two linear operators Tf=f′/αand T^*=zf to construct two self-adjoint operators A and B such that[A,B]is a scalar multiple of the identity operator on Fα^2,and obtain some more accurate results about the uncertainty principles for theα-fock space Fα^2,where T^*is the adjoint of T,[A,B]=AB-BA is the commutator of A and B,which extends and completes the results of Qu[1]and Zhu[2].