Decay of the Fourier transform of surfaces with vanishing curvature
Decay of the Fourier transform of surfaces with vanishing curvature
复制标题
曲率消失的曲面傅里叶变换的衰减
DOI：
10.1007/s00209-007-0125-4
复制
发表时间：
2006
影响因子：
0.8
通讯作者：
M. Salmhofer
中科院分区：
文献类型：
--
作者：
L. Erdős;M. Salmhofer
本文证明了二维曲面上测度μ的Fourier变换的Lp-界。我们的方法允许考虑表面上的高斯曲率消失的一维子流形。在一定的非退化条件下，证明了β > 0，并给出了L4-范数的一个代数发散界.我们使用后者的限制，估计几乎奇异积分涉及的色散关系，离散拉普拉斯算子的立方晶格。我们简要地解释了我们的动机，这个界限起源于随机薛定谔算子理论。
We proveLp-bounds on the Fourier transform of measures μ supported on two dimensional surfaces. Our method allows to consider surfaces whose Gauss curvature vanishes on a one-dimensional submanifold. Under a certain non-degeneracy condition, we prove that, β > 0, and we give a logarithmically divergent bound on theL4-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation,, of the discrete Laplace operator on the cubic lattice. We briefly explain our motivation for this bound originating in the theory of random Schrödinger operators.