FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 207-223

S. S. Platonov

Abstract

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```
Let
```$M$ be a compact symmetric space of rank $1$ . We have
defined the Nikolskii--Besov function classes
$B_{p,\theta}^r(M)$ ,
$r > 0$ ,
$1 \leq \theta \leq \infty$ ,
$1 \leq p \leq \infty$ , and
we have obtained a constructive description of these classes
in terms of the best approximations of functions
$f\in L_p(M)$
by the spherical polynomials on $M$ .

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