Decay of the Fourier transform of surfaces with vanishing curvature
| dc.creator | Erdos, Laszlo | |
| dc.creator | Salmhofer, Manfred | |
| dc.date | 2006-04-18 | |
| dc.date.accessioned | 2026-07-07T07:10:20Z | |
| dc.date.available | 2026-07-07T07:10:20Z | |
| dc.description | We prove $L^p$-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 $\whμ\in L^{4+β}$, $β>0$, and we give a logarithmically divergent bound on the $L^4$-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation, $e(p)= \sum_1^3 [1-\cos p_j]$, 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. | |
| dc.description | 40 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0604039 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0604039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111389 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 42B10, 81T18 | |
| dc.title | Decay of the Fourier transform of surfaces with vanishing curvature | |
| dc.type | text |