| Abstract: |
| Sampling series are employed in signal processing and in approximation theory to reconstruct or approximate functions from their values on discrete sets of points. One of the first results in this context is the Whittaker-Kotel'nikov-Shannon theorem for bandlimited functions. Variations of classical sampling series replace pointwise evaluations with integral averages providing flexibility, for instance, in contrast to noise. A common characteristic is the definition in terms of a so-called kernel, which may belong to various spaces of functions. In this talk we will make an overview of sampling-type series and discuss the problem of approximating differential operators. |
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