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Reconstruction of Entire Functions From Irregularly Spaced Sample Points

Published online by Cambridge University Press:  20 November 2018

Georgi R. Grozev  and
Qazi I. Rahman
Georgi R. Grozev
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, H3C 3J7, e-mail: georgig@numetrix.com, e-mail: rahmanqi@ere.umontreal.ca
Qazi I. Rahman
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, H3C 3J7, e-mail: georgig@numetrix.com, e-mail: rahmanqi@ere.umontreal.ca
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Abstract

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Let where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.

Keywords

30D1030D1541A0594A05entire functions of exponential typeWhittaker-Shannon sampling theoremnonuniform samplingmultidimensional samplinginterpolation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 777 - 793
Copyright
Copyright © Canadian Mathematical Society 1996

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