## Konvergenzverhalten der konjugierten Shannonschen Abtastreihe (Convergence behavior of the conjugate Shannon sampling series).(German)Zbl 0931.42024

Summary: This paper deals with a question proposed by F. Schipp, regarding the convergence behavior of the conjugate Shannon sampling series for non-bandlimited functions. The convergence behavior is characterized according to the Sobolev spaces $$H^s(\mathbb R)$$. If $$s>\frac 12$$ then the sequence of the conjugate Shannon sampling series is uniformly convergent for all elements of the space $$H^s(\mathbb R)$$. If $$s<\frac 12$$ then a function $$f_1 \in H^s (\mathbb R)$$ will be constructed, so that the sequence of the conjugate Shannon sampling series is divergent everywhere. The Hilbert transform $$f_1$$ is a continuous function.

### MSC:

 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 41A05 Interpolation in approximation theory 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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### References:

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