This article is cited in 14 papers

How Best to Recover a Function from Its Inaccurately Given Spectrum?

G. G. Magaril-Il'yaev, K. Yu. Osipenko

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: Consider the problem of optimal recovery of a function and its derivatives on the line from the Fourier transform of the function known approximately on a set of finite measure. We find an optimal recovery method and an optimal set on which we must measure the Fourier transform with given error.

Keywords: optimal recovery of a function, Fourier transform, Sobolev class of functions, Lagrange function.

UDC: 517.984.64

Received: 17.11.2010

DOI: 10.4213/mzm9042

 English version: Mathematical Notes, 2012, 92:1, 51–58

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