We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we investigate the growth of the information complexity as $d\to\infty$. The asymptotics are obtained for the case of fixed error threshold and for the case when it goes to zero as $d\to\infty$.

翻译：我们考虑定义在$\mathbb{R}^d$上且属于具有常数形状参数的张量积型再生高斯核希尔伯特空间的$d$元函数逼近问题。在最坏情况框架下，我们研究当$d\to\infty$时信息复杂度的增长趋势。分别针对固定误差阈值和误差阈值随$d\to\infty$趋于零两种情况，获得了渐近结果。