Cardinal Interpolation with Gaussian Kernels
Cardinal Interpolation with Gaussian Kernels
复制标题
使用高斯核的基数插值
DOI：
10.1007/s00041-011-9185-2
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发表时间：
2010
影响因子：
1.2
通讯作者：
Joseph D. Ward
中科院分区：
文献类型：
--
作者：
T. Hangelbroek;W. Madych;F. Narcowich;Joseph D. Ward
本文研究了高斯核的尺度多整数平移插值问题。主要结果建立了Lp Sobolev误差估计，并表明误差由与基数插值密切相关的傅里叶乘数的Lp乘子范数控制，并且与Hilbert变换相当。因此，当1<p<∞时，其乘子范数是有界的，与网格间距无关，当p=1或∞时，其乘子范数包含对数项。
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes Lp Sobolev error estimates and shows that the error is controlled by the Lp multiplier norm of a Fourier multiplier closely related to the cardinal interpolant, and comparable to the Hilbert transform. Consequently, its multiplier norm is bounded independent of the grid spacing when 1<p<∞, and involves a logarithmic term when p=1 or ∞.