inverse of operator

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I want to calculate the inverse of the operator $T=-\frac{\partial^{2} }{\partial x^{2}}-\frac{\partial^{2}}{\partial y^{2}}-(x^{2}+y^{2})+2( x\frac{\partial }{\partial y}-y\frac{\partial }{\partial x} )$ with domain $D=C^{\infty}_{c}$. Can you give me some methods, thanks in advance