Determination of a convex body from Minkowski sums of its projections

Journal of the London Mathematical Society

Volumn 70, Issue 2, 2004, Pages 529-544

  Kiderlen, Markus ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7544245240     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610704005551     Document Type: Article

References (17)

1. G. E. ANDREWS, R. ASKEY and R. RANJAN, Special functions (Cambridge University Press, Cambridge, 1999).
2. C. BERG, 'Corps convexes et potentiels sphériques', Mat.-Fys. Medd. Danske Vid. Selsk. 37 (1969).
3. S. CAMPI, 'Reconstructing a convex surface from certain measurements of its projections', Boll. Un. Mat. Ital. B 5 (1986) 945-959.
4. P. GOODEY, 'Minkowski sums of projections of convex bodies', Mathematics 45 (1998) 253-268.
5. P. GOODEY and H. GROEMER. 'Stability results for first order projection bodies'. Proc. Amer. Math. Soc. 109 (1990) 1103-4114.
6. P. GOODEY and W. JIANG, 'Minkowski sums of three dimensional projections of convex bodies', Rend. Circ. Mat. Palermo (2) Suppl. 65 (2000) 105-119 (Proceedings of the Third International Conference on Stochastic Geometry, Convex Bodies and Empirical Measures, Italy, 1999. Part II: Convex bodies (ed. P. M. Gruber)).
7. P. GOODEY and W. WEIL, 'Centrally symmetric convex bodies and the spherical Radon transform', J. Differential Geom. 35 (1992) 675-688.
8. H. GROEMER, 'Geometric applications of Fourier series and spherical harmonics', Encyclopedia of mathematics and its applications (Cambridge University Press, Cambridge. 1996).
9. M. KIDERLEN, 'Blaschke and Minkowski endomorphisms of convex bodies', in preparation.
10. H. MINKOWSKI, Über die Körper konstanter Breite (Teubner, 1911) 277-279.
11. R. SCHNEIDER, 'Equivariant endomorphisms of the space of convex bodies', Trans. Amer. Math. Soc. 194 (1974) 53-78.
12. R. SCHNEIDER, 'Rekonstruktion eines konvexen Körpers aus seinen Projektionen', Math. Nachr. 79 (1977) 325-329.
13. R. SCHNEIDER, 'Convex bodies: the Brunn-Minkowski theory', Encyclopedia of mathematics and its applications (Cambridge University Press, Cambridge, 1993).
14. R. SCHNEIDER, 'On the mean normal measure of a particle process', Adv. in Appl. Probab. 33 (2001) 25-38.
15. R. T. SEELEY, 'Spherical harmonics', Amer. Math. Monthly 73 (1966) 115-121.
16. K. K. SPRIESTERSBACH, 'Determination of a convex body from the average of projections and stability results', Math. Proc. Cambridge Philos. Soc. 123 (1998) 561-569.
17. p metrics for compact convex sets', J. Approx. Theory 45 (1985) 280-287.