Geodesic
Approximations on compact symmetric spaces of rank~1
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 753-769

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On an arbitrary Riemannian symmetric space $M$ of rank 1 the Nikol'skii classes $H_p^r(M)$ are defined by considering differences along geodesics. These spaces are described in terms of the best approximations by polynomials in spherical harmonics on $M$, that is, by linear combinations of the eigenfunctions of the Laplace–Beltrami operator on $M$. The results of Nikol'skii and Lizorkin on the approximation of functions on the sphere $S^n$ are generalized. 
@article{SM_1997_188_5_a5,
     author = {S. S. Platonov},
     title = {Approximations on compact symmetric spaces of rank~1},
     journal = {Sbornik. Mathematics},
     pages = {753--769},
     publisher = {mathdoc},
     volume = {188},
     number = {5},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_5_a5/}
}
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S. S. Platonov. Approximations on compact symmetric spaces of rank~1. Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 753-769. http://geodesic.mathdoc.fr/item/SM_1997_188_5_a5/