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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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What kind of functions can be represented as infinite linear combinations of exponential fun...

Let $f(x)$ be a real-valued function defined in $(0, \infty)$. I am curious what kind of $f(x)$ has the following representations: $$ f(x) = \sum_{j=0}^\infty a_j e^{-jx}, \quad \forall x \in (0, \inf …
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