THE CRAMER-WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRS
Language
en
Article de revue
This item was published in
Journal de l'Institut de Mathématiques de Jussieu. 2020, vol. 19, p. 117-135
English Abstract
Two measurable sets S, Λ ⊆ R d form a Heisenberg uniqueness pair, if every bounded measure µ with support in S whose Fourier transform vanishes on Λ must be zero. We show that a quadratic hypersurface and the union of two ...Read more >
Two measurable sets S, Λ ⊆ R d form a Heisenberg uniqueness pair, if every bounded measure µ with support in S whose Fourier transform vanishes on Λ must be zero. We show that a quadratic hypersurface and the union of two hyperplanes in general position form a Heisenberg uniqueness pair in R d. As a corollary we obtain a new, surprising version of the classical Cramér-Wold theorem: a bounded measure supported on a quadratic hypersurface is uniquely determined by its projections onto two generic hyperplanes (whereas an arbitrary measure requires the knowledge of a dense set of projections). We also give an application to the unique continuation of eigenfunctions of second-order PDEs with constant coefficients .Read less <
English Keywords
Heisenberg Uniqueness
Cramer-Wold theorem
Unique continuation
ANR Project
Géométrie des mesures convexes et discrètes - ANR-11-BS01-0007
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Origin
Hal imported