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The classical Paley–Wiener space possesses two reproducing formulae; a 'concrete' reproducing equation and a 'discrete' analogue, or sampling series, and there is a striking comparison between them. It is shown that such analogies persist in the setting of Paley–Wiener spaces that are more general than the classical case. In fact, there are 'operator'(More)
This paper discusses the work of Herbert Raabe (1909–2004) and its significance in terms of sampling. Raabe's thesis, published in 1939, represents a milestone in the development of sampling, as pointed out in the historical works of L ¨ uke. Raabe built and analysed the first time-division multiplex system for telephony, a task that required of him a(More)
Acknowledgments This publication draws on the ideas and expertise of many individuals across the country who graciously committed their time and efforts to assist in its development. It would be impossible to acknowledge individually all who contributed. The American Probation and Parole Association (APPA) would like to express special appreciation,(More)
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