The Best Approximation of a Set Whose Elements Are Known Approximately

This paper is concerned with the problem of the best (in a precisely defined sense) approximation with given accuracy of periodic functions and functions on the real line from, respectively, a finite tuple of noisy Fourier coefficients or noisy Fourier transform on an arbitrary set of finite measure...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016-11, Vol.218 (5), p.636-646
Main Authors: Magaril-Il’yaev, G. G., Osipenko, K. Yu, Sivkova, E. O.
Format: Article
Language:English
Subjects:
Approximation
Fourier transforms
Mathematical analysis
Mathematics
Mathematics and Statistics
Periodic functions
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Description
Summary:This paper is concerned with the problem of the best (in a precisely defined sense) approximation with given accuracy of periodic functions and functions on the real line from, respectively, a finite tuple of noisy Fourier coefficients or noisy Fourier transform on an arbitrary set of finite measure.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-3047-z