Given $f \in C^{\infty}_{0}[a, b]\cap L^{2}(\mathbb{R})$, what can we say about the convergence rate of the cardinal series $$ s(t) = \sum_{j=0}^{n-1} f(a+jh) \mathrm{sinc}\left(\pi\left(\frac{t-a}{h} -j \right)\right) $$ to $f$ as $h\to 0$?
2026-03-25 22:03:53.1774476233
Convergence rate of cardinal series
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