Geodesic
Localized polynomial bases on the sphere
Electronic transactions on numerical analysis, Tome 19 (2005), pp. 84-93
The subject of many areas of investigation, such as meteorology or crystallography, is the reconstruction of a continuous signal on the -sphere from scattered data. A classical approximation method is $polynomial\textcent interpolation$. Let denote the space of polynomials of degree at most on the unit sphere . As it is $\sterling $############# §$\copyright \ddot $ well known, the so-called $spherical harmonics$ form an orthonormal basis of the space . Since these functions $\sterling $### exhibit a poor localization behavior, it is natural to ask for better localized bases. Given , "! 7§$8\ddot #\\%(' ) ) ) ' 0 \%4365 $textcent$CQ2RTS $
Classification : 41A05, 65D05, 15A12
Keywords: fundamental systems, localization, matrix condition, reproducing kernel 
@article{ETNA_2005__19__a3,
     author = {La{\'\i}n Fern\'andez,  Noem{\'\i}},
     title = {Localized polynomial bases on the sphere},
     journal = {Electronic transactions on numerical analysis},
     pages = {84--93},
     year = {2005},
     volume = {19},
     zbl = {1083.41003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/}
}
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AU  - Laín Fernández,  Noemí
TI  - Localized polynomial bases on the sphere
JO  - Electronic transactions on numerical analysis
PY  - 2005
SP  - 84
EP  - 93
VL  - 19
UR  - http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/
LA  - en
ID  - ETNA_2005__19__a3
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%0 Journal Article
%A Laín Fernández,  Noemí
%T Localized polynomial bases on the sphere
%J Electronic transactions on numerical analysis
%D 2005
%P 84-93
%V 19
%U http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/
%G en
%F ETNA_2005__19__a3
Laín Fernández,  Noemí. Localized polynomial bases on the sphere. Electronic transactions on numerical analysis, Tome 19 (2005), pp. 84-93. http://geodesic.mathdoc.fr/item/ETNA_2005__19__a3/