Aarhus Universitets segl

Integral Transforms in Geometric Tomography

by Paul Goodey, Markus Kiderlen and Wolfgang Weil
Research Reports Number 498 (August 2007)
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.
Format available: PDF (373 KB)
Published in Adv. Geom. 11 (2011), 1-47, with the new title "Spherical Projections and Liftings in Geometric Tomography".
This primarily serves as Thiele Research Reports number 11-2007, but was also published in Research Reports