加权Fock空间F2α上的测不准原理的推广

摘要

对α＞0,本文主要研究了复平面上的加权Fock空间F2α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F2α上构造了两个线性算子Tf=f'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F2α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,for α ＞ 0,we characterize several versions uncertainty principles of self-adjoint operators and linear operators for the α-fock space Fα2 in the complex plane.By using the general result from functional analysis,we find two linear operators Tf =f'/α and T* =zf to construct two self-adjoint operators A and B such that [A,B] is a scalar multiple of the identity operator on F2α,and obtain some more accurate results about the uncertainty principles for the α-fock space F2α,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].