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Reconstructing curves from sets of quantized observations

Published online by Cambridge University Press:  26 February 2010

A. G. Amercrombie
Affiliation:
Department of Pure Mathematics, University of Liverpool, P. O. Box 147, Liverpool L69 3BX.
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Extract

For arbitrary f: RR and ϒ ⊂ Z × R we define the set of quantized observations of f relative to ϒ as follows: for each integer n and each yR we write

(the supremum of an empty set is taken to be −∞ ) and we put

Thus for example and , where [x] (without subscript) denotes as usual the integer part of x.

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Type
Research Article
Copyright
Copyright © University College London 1995

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