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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

$ L^{p}$ approximation of Fourier transforms and certain interpolating splines

Author: David C. Shreve
Journal: Math. Comp. 28 (1974), 779-787
MSC: Primary 65T05; Secondary 42A68
MathSciNet review: 0383803
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Abstract: We extend to $ {L^p},1 \leqq p \leqq \infty $, the $ {L^2}$ results of Bramble and Hilbert on convergence of discrete Fourier transforms and on approximation using smooth splines. The main tools are the estimates of [1] for linear functionals on Sobolev spaces and elementary results on Fourier multipliers.

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PII: S 0025-5718(1974)0383803-4
Article copyright: © Copyright 1974 American Mathematical Society