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Determination of Convex Bodies by Directed Projection Functions

Part of: General convexity

Published online by Cambridge University Press:  21 December 2009

Paul Goodey  and
Wolfgang Weil
Paul Goodey
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A. E-mail: pgoodey@ou.edu
Wolfgang Weil
Affiliation:
Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany. E-mail: weil@math.uni-karlsruhe.de
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Abstract

A tensor-type integral formula for intrinsic volumes is used to define a further variant of directed projection functions and show that these determine a convex body uniquely. Averages of directed projection functions are then studied, and the connections between the resulting operators and previously considered spherical transforms discussed.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 52A22: Random convex sets and integral geometry
Type
Research Article
Information
Mathematika , Volume 53 , Issue 1 , June 2006 , pp. 49 - 69
Copyright
Copyright © University College London 2006

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