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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Approximation of smooth compactly supported functions on $\mathbb{R}^2$ using sums of produc...

Let $f \in C^{\infty}(\mathbb{R}^2)$ be smooth and compactly supported. Can we approximate $f(x,y)$ by sums of the form $\sum_{i=1}^m g_i(x) h_i (y)$ where $g_i, h_i \in C^{\infty}(\mathbb{R})$ are s …
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