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Let $M$ be a compact connected smooth manifold. Write $C^{\infty}(M)$ for the Frechet space of the smooth real-valued functions on $M$ equipped with the usual $C^{\infty}$-topology. Given a compact ...

Let $\epsilon>0$ be small. Let $\eta(t) = \frac{2\epsilon}{\epsilon^2+(2\pi t)^2}$ (the Fourier transform of $x\mapsto e^{-\epsilon |x|}$). Let $V$ be the space of integrable, bounded functions $f:\...