I want to prove or disprove that the Fourier transform $ \mathcal F \colon (\mathcal S(\mathbb R^d), \lVert \cdot \rVert_1) \to L^1(\mathbb R^d)$ is unbounded, where $ \lVert\cdot \rVert_1$ denotes the $ L^1(\mathbb R^d)$ -norm. Having thought about this for a moment, I believe it is indeed unbounded. So I tried to find a sequenceRead more