Fourier transform of surface--carried measures of two-dimensional generic surfaces and applications
Analysis of PDEs
2021-07-29 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose characteristic surfaces satisfy the generic assumptions. We also obtain new results on the spectral and scattering theory of discrete Schr\"odinger operators on the cubic lattice.
Keywords
Cite
@article{arxiv.2107.13400,
title = {Fourier transform of surface--carried measures of two-dimensional generic surfaces and applications},
author = {Jean-Claude Cuenin and Robert Schippa},
journal= {arXiv preprint arXiv:2107.13400},
year = {2021}
}