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Determination of Convex Bodies by Directed Projection Functions
Author(s) -
Goodey Paul,
Weil Wolfgang
Publication year - 2006
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000024
Subject(s) - mathematics , projection (relational algebra) , regular polygon , convex body , convex analysis , mathematical analysis , pure mathematics , convex optimization , geometry , algorithm
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.