Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation

Previous article Next article Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline InterpolationJ. H. Bramble and S. R. HilbertJ. H. Bramble and S. R. Hilberthttps: //doi. org/10. 1137/0707006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 G. Birkhoff, , M. H. Schultz and, R. S. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations, Numer. Math. , 11 (1968), 232–256 10. 1007/BF02161845 MR0226817 0159. 20904 CrossrefISIGoogle Scholar2 J. H. Bramble, , B. E. Hubbard and, Vidar Thomée, Convergence estimates for essentially positive type discrete Dirichlet problems, Math. Comp. , 23 (1969), 695–709 MR0266444 0217. 21902 CrossrefISIGoogle Scholar3 Michael Golomb, Approximation by periodic spline interpolants on uniform meshes, J. Approximation Theory, 1 (1968), 26–65 10. 1016/0021-9045 (68) 90055-5 MR0233121 0185. 30901 CrossrefGoogle Scholar4 Charles B. Morrey, Jr. , Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc. , New York, 1966ix+506 MR0202511 0142. 38701 CrossrefGoogle Scholar5 Arthur Sard, Linear approximation, American Mathematical Society, Providence, R. I. , 1963xi+544, Math. Surveys, No. 9 MR0158203 0115. 05403 CrossrefGoogle Scholar6 I. J. Schoenberg, On cardinal spline interpolation and a summability method for the cardinal series, Symposium on Approximation, Lecture Notes, University of Cincinnati, Cincinnati, Ohio, 1969 Google Scholar7 J. M. Whittaker, Interpolatory Function Theory, Cambridge University Press, Cambridge, 1935 0012. 15503 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Interpolated Galerkin Finite Element Method for the Poisson EquationJournal of Scientific Computing, Vol. 92, No. 2 | 30 June 2022 Cross Ref Virtual element approximation of two-dimensional parabolic variational inequalitiesComputers & Mathematics with Applications, Vol. 116 | 1 Jun 2022 Cross Ref Direct serendipity and mixed finite elements on convex quadrilateralsNumerische Mathematik, Vol. 150, No. 4 | 26 March 2022 Cross Ref Nonlinear systems of parabolic IBVP: A stable super-supraconvergent fully discrete piecewise linear FEMApplied Mathematics and Computation, Vol. 419 | 1 Apr 2022 Cross Ref Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic MapsXinping Gui, Buyang Li, and Jilu WangSIAM Journal on Numerical Analysis, Vol. 60, No. 1 | 8 February 2022AbstractPDF (572 KB) 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