Support Theorems for the Radon Transform and Cramér-Wold Theorems

Basrak, B., Davis, R., Mikosch, T.: A characterization of multivariate regular variation. Ann. Appl. Probab. 12, 908–920 (2002)

Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968)

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)

Boman, J.: Holmgren’s uniqueness theorem and support theorems for real analytic Radon transforms. Contemp. Math. 140, 23–30 (1992)

Cramér, H., Wold, H.: Some theorems on distribution functions. J. Lond. Math. Soc. 11, 290–294 (1936)

Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Springer, New York (1988)

Folland, G.B.: Real Analysis: Modern Techniques and Their Applications. Wiley, New York (1999)

Gelfand, I.M., Shilov, G.E.: Generalized Functions I, Properties and Operations. Academic Press, New York (1964)

Gelfand, I.M., Gindikin, S., Graev, M.I.: Integral geometry in affine and projective spaces. J. Sov. Math. 18, 39–167 (1982)

Helgason, S.: The Radon Transform. Birkhäuser, Boston (1980)

Hörmander, L.: The Analysis of Linear Partial Differential Operators I, 2nd edn. Springer, Berlin (2003)

Hult, H., Lindskog, F.: On Kesten’s counterexample to the Cramér-Wold device for regular variation. Bernoulli 12, 133–142 (2006)

Hult, H., Lindskog, F.: Regular variation for measures on metric spaces. Publ. Inst. Math. (Belgr.) 80, 121–140 (2006)

Kesten, H.: Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207–248 (1973)

Meerschaert, M.M., Scheffler, H.-P.: Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley, New York (2001)

Palamodov, V.P.: Inversion Formula for the Three-Dimensional Ray Transform. Lecture Notes in Mathematics, vol. 1497, pp. 53–62. Springer, Berlin (1989)

Palamodov, V.P.: Reconstruction from line integrals in spaces with constant curvature. Math. Nachr. 196, 167–188 (1998)

Palamodov, V.P.: Reconstructive Integral Geometry. Birkhäuser, Boston (2004)

Resnick, S.I.: Extreme Values, Regular Variation, and Point Processes. Springer, New York (1987)

Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1966)

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)

Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)

Schwartz, L.: Théorie des Distributions. Hermann, Paris (1950)

Strichartz, R.S.: Radon inversion—variation on a theme. Am. Math. Mon. 89, 377–423 (1982)

Weiss, B.: Measures that vanish on half spaces. Proc. Am. Math. Soc. 18, 123–126 (1967)