학술논문
The Euler characteristic of a surface from its Fourier analysis in one direction.
Document Type
Journal
Author
Dang, Nguyen Viet (F-ULIL-LM) AMS Author Profile
Source
Subject
42 Harmonic analysis on Euclidean spaces -- 42B Harmonic analysis in several variables
42B08Summability
42B08
Language
English
Abstract
Summary: ``In this paper, we prove that we can recover the genus of a closed compact surface $S$ in $\Bbb{R}^{3}$ from the restriction to a generic line of the Fourier transform of the canonical measure carried by $S$. We also show that the restriction on some line in Minkowski space of the solution of a linear wave equation whose Cauchy data comes from the canonical measure carried by $S$, allows to recover the Euler characteristic of $S$.''