Artículos de revistas
Approximation In L2 Sobolev Spaces On The 2-sphere By Quasi-interpolation
Registro en:
Journal Of Fourier Analysis And Applications. , v. 7, n. 3, p. 282 - 295, 2001.
10695869
2-s2.0-0346485761
Autor
Gomes S.M.
Kushpel A.K.
Levesley J.
Institución
Resumen
In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ℝ3, and present rates of convergence for this method in Sobolev spaces of square integrable functions. We write the discrete Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete Fourier projection. We also discuss some typical practical examples used in the context of spherical wavelets. 7 3 282 295 Abramowitz, M., Stegun, I.A., (1964) Handbook of Mathematical Functions, , National Bureau of Standards, Dover Publications Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, G., Higher Transcendental Functions (1953) The Bateman Manuscript Project, 2. , McGraw-Hill Driscoll, J.R., Healy, D.M., Computing Fourier transforms and convolutions on the 2-sphere (1994) Advances in Applied Mathematics, 15, pp. 202-250 Fasshauer, G.E., Schumaker, L.L., Scattered data fitting on the sphere (1998) Mathematical Methods for Curves and Surfaces, II, pp. 117-166. , (Lillehammer, 1997), Innov. Appl. Math., Vanderbilt University Press, Nashville, TN Freeden, W., Gervens, T., Schreiner, M., (1998) Constructive Approximation on the Sphere, , Claredon Press Freeden, W., Windheuser, U., Combined spherical harmonic and wavelet expansion - A future concept in earth's gravitational determination (1997) Appl. Comput. Harmon. Anal., 4, pp. 1-37 Kushpel, A.K., Levesley, J., Quasi-interpolation on the 2-sphere using radial polynomials (2000) J. Approx. Theory, 102, pp. 141-154 Muller, C., Spherical harmonics (1966) Lecture Notes in Mathematics, 17. , Springer Verlag Orzag, S.A., Transform method for the calculation of vector-coupled sums: Applications to spectral form of the vorticity equation (1970) J. Atmosph. Sci., 27, pp. 890-895 Potts, D., Steidl, G., Tasche, M., Kernels of spherical harmonics and spherical frames (1996) Advanced Topics in Multivariate Approximation, , Fontanella, F., et al., Eds., World Science Publishing, River Edge, NJ Powell, M.J.D., The theory of radial basis functions in 1990 (1992) Advances in Numerical Analysis II: Wavelets, Subdivision, and Radial Basis Functions, , Light, W.A., Ed., Oxford University Press, Oxford Reimer, M., Hyperinterpolation on the sphere at the minimal projection order (2000) J. Approx. Theory, 104, pp. 272-286 Schreiner, M., A pyramid scheme for spherical wavelets (1996) AGTM Report 170, , University of Kaiserslauten Sloan, I.H., Interpolation and hyperinterpolation on the sphere (1997) Multivariate Approximation, pp. 255-268. , (Witten-Bommerholz, 1996) Math. Res., 101. , Akademie Verlag, Berlin Szegö, G., (1959) Orthogonal Polynomials, 23. , American Mathematical Society Colloquium Publications American Mathematical Society, Providence, RI Jakob-Chien, R., Hack, J.J., Williamson, D.L., Spectral transform solutions to shallow water test sets (1995) J. Comp. Physics, 119, pp. 164-187