Sampling Problem for Non-separated Sets and Divided Differences

An approach to solving sampling and interpolation problems in the case of non-separated sequences is developed. The approach is based on the duality between Riesz bases of exponential divided differences and group sampling and interpolating sequences. The complete description of group sampling and i...

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Bibliographic Details
Published inSampling theory in signal and image processing Vol. 8; no. 2; pp. 181 - 199
Main Authors Avdonin, S.A., Ivanov, S.A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.05.2009
Sampling Publishing
Subjects
Abstract Harmonic Analysis
Duality theory (Mathematics)
Functions, Exponential
Image and Speech Processing
Interpolation
Machine Learning
Mathematics
Methods
Signal
Statistical sampling
interpolation
30B50
42A99
families of exponentials
Riesz bases
Sampling
94A12
divided differences
94A20
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ISSN1530-6429
DOI10.1007/BF03549514

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Summary:An approach to solving sampling and interpolation problems in the case of non-separated sequences is developed. The approach is based on the duality between Riesz bases of exponential divided differences and group sampling and interpolating sequences. The complete description of group sampling and interpolating sequences for the Paley-Wiener spaces is obtained and stability properties of these sequences are discussed.
ISSN:1530-6429
DOI:10.1007/BF03549514