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Markus Kiderlen

Spherical projections and liftings in geometric tomography

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  • Paul Goodey, University of Oklahoma, United States
  • Markus Kiderlen
  • Wolfgang Weil, University of Karlsruhe, Germany
  • Department of Mathematical Sciences
  • T.N. Thiele Centre
  • Centre for Stochastic Geometry and Advanced Bioimaging
We consider a variety of integral transforms arising in Geometric
Tomography. It will be shown that these can be put into a common
framework using spherical projection and lifting operators. These
operators will be applied to support functions and surface area
measures of convex bodies and to radial functions of star bodies. We
then investigate averages
of lifted projections and show that they correspond to self-adjoint
intertwining operators. We obtain formulas for the eigenvalues of
these operators and use them to ascertain circumstances under which
tomographic measurements determine the original bodies. This
approach via mean lifted projections leads us to some unexpected
relationships between seemingly disparate geometric constructions.

Original languageEnglish
JournalAdvances in Geometry
Volume11
Issue1
Pages (from-to)1-47
Number of pages47
ISSN1615-715X
DOIs
Publication statusPublished - 2011

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