Confirmation of Matheron's conjecture on the covariogram of a planar convex body

Mathematics – Metric Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

12 pages, 7 figures

Scientific paper

The covariogram g_K of a convex body K in E^d is the function which associates to each x in E^d the volume of the intersection of K with K+x. In 1986 G. Matheron conjectured that for d=2 the covariogram g_K determines K within the class of all planar convex bodies, up to translations and reflections in a point. This problem is equivalent to some problems in stochastic geometry and probability as well as to a particular case of the phase retrieval problem in Fourier analysis. It is also relevant for the inverse problem of determining the atomic structure of a quasicrystal from its X-ray diffraction image. In this paper we confirm Matheron's conjecture completely.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Confirmation of Matheron's conjecture on the covariogram of a planar convex body does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Confirmation of Matheron's conjecture on the covariogram of a planar convex body, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Confirmation of Matheron's conjecture on the covariogram of a planar convex body will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-659779

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.