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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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IMPACT FACTOR 2016: 0.552

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Online
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1615-7168
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Volume 11, Issue 1 (Jan 2011)

Issues

Spherical projections and liftings in geometric tomography

Paul Goodey / Markus Kiderlen / Wolfgang Weil
Published Online: 2011-01-07 | DOI: https://doi.org/10.1515/advgeom.2010.037

Abstract

We use spherical projection and lifting operators in Euclidean d-space to describe a general framework for a variety of integral transforms arising in geometric tomography. 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.

About the article

Received: 2008-09-23

Published Online: 2011-01-07

Published in Print: 2011-01-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.037.

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Citing Articles

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[1]
Daniel Hug and Rolf Schneider
Archiv der Mathematik, 2015, Volume 104, Number 1, Page 83
[2]
Stefano Campi, Richard J. Gardner, Paolo Gronchi, and Markus Kiderlen
Advances in Mathematics, 2012, Volume 231, Number 6, Page 3118
[3]
Paul Goodey and Wolfgang Weil
Advances in Mathematics, 2012, Volume 229, Number 1, Page 596

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