Classical and approximate sampling theorems; studies in the \(L^{p}(\mathbb R)\) and the uniform norm. (English) Zbl 1089.94013
It is known that the approximate sampling theorem implies the Shannon theorem. This paper proves the converse. Note that those two important theorems are equivalent in the uniform sense. The authors consider the same problems in \(L^p\) norm and show that one implication still holds.
Reviewer: Youming Liu (Beijing)
MSC:
| 94A20 | Sampling theory in information and communication theory |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 41A80 | Remainders in approximation formulas |
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