Jackson-type theorems for compact symmetric spaces of rank 1 (Q2714066)

The author studies certain problems of the approximation theory for functions on compact symmetric spaces \(M\) of rank 1. The aim of the article is to prove Jackson-type theorems for an arbitrary \(M\). The main result of the article reads as follows:NEWLINENEWLINENEWLINETheorem. Let \(f(x)\in L_p(M)\) be \(r\) times differentiable in \(L_p(B)\). Then the following inequality holds: NEWLINE\[NEWLINE E_N(f)_p \leq \frac{c_2}{N^r}\omega_k\left(f^{(r)},\frac{\pi}{N}\right)_p, \quad N = 1, 2,\dots, NEWLINE\]NEWLINE where \(c_2\) is a constant independent of \(f\) and \(N\).