Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data

DOI10.1215/S0012-7094-01-10714-XzbMath1010.35001MaRDI QIDQ1847812

Eric Todd Quinto, Mark L. Agranovsky

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Coxeter setfinitely supported distributions

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Wave equation (35L05) Radon transform (44A12) Fourier integral operators applied to PDEs (35S30)

Related Items (8)

Range descriptions for the spherical mean Radon transform ⋮ Stationary sets for the wave equation in crystallographic domains ⋮ Harmonic divisors and rationality of zeros of Jacobi polynomials ⋮ Image reconstruction from radially incomplete spherical Radon data ⋮ Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations ⋮ Mathematics of thermoacoustic tomography ⋮ The Khavinson-Shapiro conjecture and polynomial decompositions ⋮ The Khavinson-Shapiro conjecture for domains with a boundary consisting of algebraic hypersurfaces

Cites Work

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• The invertibility of rotation invariant Radon transforms
• Nodal sets of eigenfunctions on Riemannian manifolds
• Über Membranen mit speziellen Knotenlinien
• Eigenfunctions and nodal sets
• Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators
• Pompeiu transforms on geodesic spheres in real analytic manifolds
• On Nodal Sets for Dirac and Laplace Operators
• Approximation by spherical waves in \(L^p\)-spaces
• Morera theorems for complex manifolds
• Injectivity sets for the Radon transform over circles and complete systems of radial functions
• Fourier integral operators. I
• Inégalités isopérimétriques et applications
• Nodal Sets for Eigenfunctions of the Laplacian On Surfaces
• The Dependence of the Generalized Radon Transform on Defining Measures
• Conical Uniqueness Sets for the Spherical Radon Transform
• Injectivity sets for spherical means on the Heisenberg group
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