## Reference for some de Rham cohomologies

I would like find the reference for the following elementray reslut which I would not like to write down the proof in my paper.

If $\mathcal{S}(\mathbf{R})$ is the schwartz space of $\mathbf{R}$. Let $$\Omega^\cdot_\pm(R)=e^{\pm x^2}\mathcal{S}(\mathbf{R},\Lambda^\cdot\mathbf{R}^*).$$ So, we have $$H^\cdot(\Omega^\cdot_+(R),d)=H^\cdot_{dR}(\mathbf{R}), \ \ H^\cdot(\Omega^\cdot_-(R),d)=H^\cdot_{dR,c}(\mathbf{R}).$$

I would like also the kunneth formula in this context.

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