紧黎曼流形上Kolmogorov、Gelfand和线性$n$ -宽度的估计
Estimates of Kolmogorov, Gelfand and linear $n$- widths on Compact Riemannian Manifolds
摘要：
我们确定了紧黎曼流形上$L_{p}$ -空间中单位球在Sobolev范数下的Kolmogorov宽度、Gelfand宽度和线性$n$ -宽度的较低的精确估计.正如我们以前所证明的，在紧齐次流形的情况下，这些下估计是渐近精确的。证明依赖于椭圆算子函数核的近对角局部化的双边估计。
英文摘要：
We determine lower and exact estimates of Kolmogorov, Gelfand and linear $n$-widths of unit balls in Sobolev norms in $L_{p}$-spaces on compact Riemannian manifolds. As it was shown by us previously these lower estimates are exact asymptotically in the case of compact homogeneous manifolds. The proofs rely on two-sides estimates for the near-diagonal localization of kernels of functions of elliptic operators.
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