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Reconstructing curves from sets of quantized observations

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  26 February 2010

A. G. Amercrombie
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: R → R and ϒ ⊂ Z × R we define the set of quantized observations of f relative to ϒ as follows: for each integer n and each y∈R 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.

MSC classification

Secondary: 11J99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 340 - 353
Copyright
Copyright © University College London 1995

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