Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We show that if the Radon transform of a distribution ƒ vanishes outside of an acute cone Co, the support of the distribution is contained in the union of Co and another acute cone C1, the cones are in a suitable position, and ƒ vanishes distributionally in the direction of the axis of C1, then actually supp ƒ C ⊂ Co. We show by examples that this result is sharp.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
207--213
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Mathematics Louisiana State University Baton Rouge, LA 70803, U.S.A.
Bibliografia
- [1] D.H. Armitage, M. Goldstein, Nonunique.ne.ss for the Radon transform,, Proc. Amer. Math. Soc. 117 (1993), 175-178.
- [2] J. Boman, Holmgren's uniqueness theorem and support theorems for real analytic Radon transforms, Contemp. Math. 140 (1992), 23-30.
- [3] J. Boman, F. Lindskog, Support theorems for the Radon transform, and Cramer-Wold theorems, J. Theor. Probab. 22 (2009), 683-710.
- [4] R. Estrada, Vector moment problems for rapidly decreasing functions of several variables, Proc. Amer. Math. Soc. 126 (1998), 761-768.
- [5] R. Estrada, Support theorems for Radon transforms of oscillatory distributions, Krugu-jevac J. Math. 39 (2015), 197-205.
- [6] R. Estrada, R.P. Kanwal, A distributional approach to Asymptotics. Theory and Applications, 2nd ed., Birkhauser, Boston, 2002.
- [7] R. Estrada, B. Rubin, Null spaces of Radon transforms, preprint 2015, arXiv: 1504.03766.
- [8] S. Helgason, The Radon transform in Euclidean spaces, compact two-point homogeneous spaces and Grassman manifolds, Acta Math. 113 (1965), 153-180.
- [9] S. Helgason, Geometric Analysis on Symmetric Spaces, Amer. Math. Soc, Providence, 2008.
- [10] L. Hórmander, The Analysis of Partial Differential Operators, vol. 1, Distribution Theory and Fourier Analysis, Springer Verlag, Berlin, 1983.
- [11] J. Horvath, Topological Vector Spaces and Distributions, vol. I, Addison-Wesley, Reading, Massachusetts, 1966.
- [12] D. Ludwig, The Radon transform, on Euclidean space, Comm. Pure Appl. Math. 19 (1966), 49-81.
- [13] S. Łojasiewicz, Sur la valuer et la limite d'une distribution en un point, Studia Math. 16 (1957), 1-36.
- [14] S. Łojasiewicz, Sur la fixation de variables dans une distribution, Studia Math. 17 (1958), 1-64.
- [15] A.G. Ramm, Radon transform on distributions, Proc. Japan Acad. 71 (1995), 202-206.
- [16] A.G. Ramm, A.I. Katsevich, The Radon Transform and Local Tomography, CRC Press, Boca Raton, 1996.
- [17] B. Rubin, Introduction to Radon transforms (with elements of fractional calculus and harmonic analysis), Cambridge University Press, 2015 (to appear).
- [18] R.S. Strichartz, Radon inversion - variation on a theme, Am. Math. Mon. 89 (1982), 377-384.
- [19] F. Treves, Topological Vector Spaces, Distributions, and Kernels, Academic Press, New York, 1967.
- [20] L. Zalcman, Uniqueness and nonuniqueness for the Radon transform,, Bull. London Math. Soc. 14 (1982), 241-245.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a8c436f3-3df8-4df4-809a-fbd0b83c9722