Let $h:\mathbb{R} \to \mathbb{C}$ be a complex-valued function. Also let$$\int_{-\infty}^{+\infty}|h(t)|dt<\infty$$Which is an improper Riemann integral. Is it true that $$\int_{-\infty}^{+\infty}|h(t)|^2dt$$ also exists? I couldn't find a counterexample for that. Note that here I mean Riemann integral not Lebesgue integral. The main reason for asking that question is this problem which asks "Does a stable LTI system with energy signal as input, always have energy signal as output?"
2026-04-05 18:35:10.1775414110
Square integrability of an absolute integrable function
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