Ruled nodal surfaces of Laplace eigenfunctions and injectivity sets for the spherical mean Radon transform in
Mark L. Agranovsky
Bar-Ilan University, Ramat Gan, Israel
![Ruled nodal surfaces of Laplace eigenfunctions and injectivity sets for the spherical mean Radon transform in $\mathbb R^3$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-7-issue-4.png&w=3840&q=90)
Abstract
It is proved that if a Paley–Wiener family of eigenfunctions of the Laplace operator in vanishes on a real-analytically ruled two-dimensional surface then is a union of cones, each of which is contained in a translate of the zero set of a nonzero harmonic homogeneous polynomial. If is an immersed manifold then is a Coxeter system of planes. Full description of common nodal sets of Laplace spectra of convexly supported distributions is given. In equivalent terms, the result describes ruled injectivity sets for the spherical mean transform and confirms, for the case of ruled surfaces in a conjecture from [1].
Cite this article
Mark L. Agranovsky, Ruled nodal surfaces of Laplace eigenfunctions and injectivity sets for the spherical mean Radon transform in . J. Spectr. Theory 7 (2017), no. 4, pp. 1039–1099
DOI 10.4171/JST/185