Geodesic
Approximation of functions on the sphere
Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 599-614

Voir la notice de l'article provenant de la source Math-Net.Ru

The authors consider classes $H_p^r(\sigma)$ of functions $f$ on a sphere $\sigma$, whose smoothness is determined by the properties of differences along geodesics (duly averaged) in the metric of $L_p(\sigma)$. An integral representation of a function $f \in L_p(\sigma)$ is obtained in terms of the differences mentioned. On this basis direct and inverse theorems on approximation of functions $f \in H_p^r(\sigma)$ be polynomials in spherical harmonics are established. These theorems completely characterize the class $H_p^r(\sigma)$. Bibliography: 9 titles. 
@article{IM2_1988_30_3_a7,
     author = {S. M. Nikol'skii and P. I. Lizorkin},
     title = {Approximation of functions on the sphere},
     journal = {Izvestiya. Mathematics },
     pages = {599--614},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a7/}
}
TY  - JOUR
AU  - S. M. Nikol'skii
AU  - P. I. Lizorkin
TI  - Approximation of functions on the sphere
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 599
EP  - 614
VL  - 30
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a7/
LA  - en
ID  - IM2_1988_30_3_a7
ER  - 
%0 Journal Article
%A S. M. Nikol'skii
%A P. I. Lizorkin
%T Approximation of functions on the sphere
%J Izvestiya. Mathematics 
%D 1988
%P 599-614
%V 30
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a7/
%G en
%F IM2_1988_30_3_a7
S. M. Nikol'skii; P. I. Lizorkin. Approximation of functions on the sphere. Izvestiya. Mathematics , Tome 30 (1988) no. 3, pp. 599-614. http://geodesic.mathdoc.fr/item/IM2_1988_30_3_a7/