正定Lipschitz核的本征值

The Eigenvalues of Positive Definite Lipschitz Kernels

设 G 是 R^d 中闭单位正方体,正定对称核 K(x,y)在 G×G 上满足α阶的 Lipschitz条件。本文证明,由 K(x,y)生成的积分算子 K 的本征值渐近为 O(1/(n^(1+α/d)))。

Suppose that G is an unit closed cube in Rd, and the positive definite symmetric Kernels K (x, y) satisfy a Lipschitz condition of order a on GxG . It is proved in this paper that the eigenvalues of the integral operator K generated by K(x,y) are asymptotically O