We provide the characterization of the Peetre-type K-functional on a compact two-point homogeneous space in terms of the rate of approximation of a family of multipliers operators. This extends the well known results on the spherical setting. The characterization is employed to prove that an abstract Hölder condition or finite order of differentiability assumption on generating positive kernels of integral operators implies a sharp decay rates for their eigenvalues sequences. Consequently, sharp upper bounds for the Kolmogorov n-width of unit balls in reproducing kernel Hilbert space are obtained.

中文翻译：

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一般设定下积分算子特征值的逼近工具和衰减率

我们提供了在一个紧凑的两点齐次空间上的Peetre型K函数的刻划，以乘积算子族的逼近率表示。这扩展了球形设定的众所周知的结果。该特征被用来证明在生成积分算子的正核时的抽象Hölder条件或微分假设的有限阶数意味着其特征值序列具有急剧的衰减率。因此，获得了在再生内核希尔伯特空间中单位球的Kolmogorov n宽度的尖锐上限。