论文标题
翻译不变核的正顺序扩展
Orthonormal Expansions for Translation-Invariant Kernels
论文作者
论文摘要
我们提出了一种通用的傅立叶分析技术，用于构建从$ \ m m i} _2 _2（\ m athbb {r}）$的正常基础的转换式内核的正顺序扩展。这使我们能够根据相关的laguerre函数（ii）在理性函数方面以及（iii）高斯kernel在Hermite功能方面，以（ii）Cauchy内核来得出所有半级订单的（i）Matérn内核的明确扩展。
We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions.
