关于加权希尔伯特空间上一个微分算子的注记

A Note on a Differential Operator in a Weighted Hilbert Space

利用复分析中研究柯西黎曼方程的赫曼德尔L2方法,研究了加权希尔伯特空间L2(R2,e-|x|2)上的微分算子a1∂2∂x21+a2∂2∂x22+a3∂2∂x1∂x2+a0,证明了由该算子所构成的微分方程的整体弱解的存在性,并证明了该算子的有界右逆算子的存在性。

Using Hormander L2 method for Cauchy-Riemann equations from complex analysis,we study a simple differential operator a1∂2∂x21+a2∂2∂x22+a3∂2∂x1∂x2+a0 in the weighted Hilbert space L2(R2,e-|x|2).We prove the existence of global weak solutions of the equation about the differential operator and that of a right bounded inverse of the differential operator.