Support theorems for the radon transform and Cramér-Wold theorems

Journal of Theoretical Probability

Volumn 22, Issue 3, 2009, Pages 683-710

  Boman, Jan ^a   Lindskog, Filip ^b  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Cram r Wold theorem; Radon transform

Indexed keywords

EID: 70350223723     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-008-0151-0     Document Type: Article

References (25)

1. Basrak, B., Davis, R., Mikosch, T.: A characterization of multivariate regular variation. Ann. Appl. Probab. 12, 908-920 (2002).
2. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968).
3. Boman, J.: Helgason's Support Theorem for Radon Transforms-a New Proof and a Generalization. Lecture Notes in Mathematics, vol. 1497, pp. 1-5. Springer, Berlin (1989).
4. Boman, J.: Holmgren's uniqueness theorem and support theorems for real analytic Radon transforms. Contemp. Math. 140, 23-30 (1992).
5. Cramér, H., Wold, H.: Some theorems on distribution functions. J. Lond. Math. Soc. 11, 290-294 (1936).
6. Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Springer, New York (1988).
7. Folland, G.B.: Real Analysis: Modern Techniques and Their Applications. Wiley, New York (1999).
8. Gelfand, I.M., Shilov, G.E.: Generalized Functions I, Properties and Operations. Academic Press, New York (1964).
9. Gelfand, I.M., Gindikin, S., Graev, M.I.: Integral geometry in affine and projective spaces. J. Sov. Math. 18, 39-167 (1982).
10. Helgason, S.: The Radon Transform. Birkhäuser, Boston (1980).
11. Hörmander, L.: The Analysis of Linear Partial Differential Operators I, 2nd edn. Springer, Berlin (2003).
12. Hult, H., Lindskog, F.: On Kesten's counterexample to the Cramér-Wold device for regular variation. Bernoulli 12, 133-142 (2006).
13. Hult, H., Lindskog, F.: Regular variation for measures on metric spaces. Publ. Inst. Math. (Belgr.) 80, 121-140 (2006).
14. Kesten, H.: Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207-248 (1973).
15. Meerschaert, M.M., Scheffler, H.-P.: Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley, New York (2001).
16. Palamodov, V.P.: Inversion Formula for the Three-Dimensional Ray Transform. Lecture Notes in Mathematics, vol. 1497, pp. 53-62. Springer, Berlin (1989).
17. Palamodov, V.P.: Reconstruction from line integrals in spaces with constant curvature. Math. Nachr. 196, 167-188 (1998).
18. Palamodov, V.P.: Reconstructive Integral Geometry. Birkhäuser, Boston (2004).
19. Resnick, S.I.: Extreme Values, Regular Variation, and Point Processes. Springer, New York (1987).
20. Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1966).
21. Rvačeva, E.L.: On domains of attraction of multi-dimensional distributions. In: Select. Transl. Math. Statist. and Probability, vol. 2, pp. 183-205. American Mathematical Society, Providence (1962).
22. Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999).
23. Schwartz, L.: Théorie des Distributions. Hermann, Paris (1950).
24. Strichartz, R.S.: Radon inversion-variation on a theme. Am. Math. Mon. 89, 377-423 (1982).
25. Weiss, B.: Measures that vanish on half spaces. Proc. Am. Math. Soc. 18, 123-126 (1967).