THE CRAMER-WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRSReport as inadecuate




THE CRAMER-WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRS - Download this document for free, or read online. Document in PDF available to download.

1 Fakultät für Mathematik Wien 2 IMB - Institut de Mathématiques de Bordeaux

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 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 .

Keywords : Heisenberg Uniqueness Cramer-Wold theorem Unique continuation





Author: Karlheinz Gröchenig - Philippe Jaming -

Source: https://hal.archives-ouvertes.fr/



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