Estimates of best approximation and fourier transforms in integral metrics

M. I. Ganzburg; E. R. Liflyand

doi:10.1006/jath.1995.1126

Estimates of best approximation and fourier transforms in integral metrics

M. I. Ganzburg, E. R. Liflyand

Department of Mathematics

New York University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Under some assumptions on a function F and its Fourier transform F̂ we prove new estimates of best approximation of F by entire functions of exponential type σ in L_p(ℝ), 1 ≤ p < 2. The proof is based on some inequalities for F̂ in L₁(ℝ) which may be treated as generalizations of results of Bausov and Telyakovskii. As an application we obtain exact estimates of best approximation of some infinitely differentiable functions.

Original language	English
Pages (from-to)	347-370
Number of pages	24
Journal	Journal of Approximation Theory
Volume	83
Issue number	3
DOIs	https://doi.org/10.1006/jath.1995.1126
State	Published - Dec 1995

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AB - Under some assumptions on a function F and its Fourier transform F̂ we prove new estimates of best approximation of F by entire functions of exponential type σ in Lp(ℝ), 1 ≤ p < 2. The proof is based on some inequalities for F̂ in L1(ℝ) which may be treated as generalizations of results of Bausov and Telyakovskii. As an application we obtain exact estimates of best approximation of some infinitely differentiable functions.

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Estimates of best approximation and fourier transforms in integral metrics

Abstract

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