$L^{p}$ approximation of Fourier transforms and certain interpolating splines
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- by David C. Shreve PDF
- Math. Comp. 28 (1974), 779-787 Request permission
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.References
- J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation, SIAM J. Numer. Anal. 7 (1970), 112–124. MR 263214, DOI 10.1137/0707006
- J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math. 16 (1970/71), 362–369. MR 290524, DOI 10.1007/BF02165007
- R. E. Edwards, Fourier series: a modern introduction. Vol. II, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1967. MR 0222538
- Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
- Sherwood D. Silliman, The numerical evaluation by splines of Fourier transforms, J. Approximation Theory 12 (1974), 32–51. MR 356556, DOI 10.1016/0021-9045(74)90056-2
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 779-787
- MSC: Primary 65T05; Secondary 42A68
- DOI: https://doi.org/10.1090/S0025-5718-1974-0383803-4
- MathSciNet review: 0383803