Keywords
- Real Analytic Function
- Fourier Integral Operator
- Radon Transforma
- Real Analytic Manifold
- Support Theorem
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References
Uniqueness theorems for generalized Radon transforms, in “Constructive Theory of Functions '84,” Sofia, 1984, pp. 173–176.
J. Boman, An example of non-uniqueness for a generalized Radon transform, Dept. of Math., University of Stockholm 1984:13.
J.-E. Björk, “Rings of Differential Operators,” North-Holland Publishing Comp., Amsterdam, 1979.
J. Boman and E. T. Quinto, Support theorems for real-analytic Radon transforms, Duke Math. J. 55 (1987), 943–948.
J. Boman and E. T. Quinto, Support theorems for real-analytic Radon transforms on line complexes in three-space, to appear in Trans. Amer. Math. Soc.
V. Guillemin and S. Sternberg, “Geometric Asymptotics,” Amer. Math. Soc., Providence, RI, 1977.
A. Greenleaf and G. Uhlmann, Nonlocal inversion formulas for the X-ray transform, Duke Math. J. 58 (1989), 205–240.
L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79–183.
L. Hörmander, “The analysis of linear partial differential operators, vol. 1,” Springer-Verlag, Berlin, Heidelberg, and New York, 1983.
S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153–180.
S. Helgason, “The Radon transform,” Birkhäuser, Boston, 1980.
S. Helgason, Support of Radon transforms, Adv. Math. 38 (1980), 91–100.
E. T. Quinto, On the locality and invertibility of Radon transforms, Thesis, M.I.T., Cambridge, Mass. (1978).
E. T. Quinto, The dependence of the generalized Radon transforms on the defining measures, Trans. Amer. Math. Soc. 257 (1980), 331–346.
E. T. Quinto, The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl. 91 (1983), 510–522.
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© 1991 Springer-Verlag Berlin Heidelberg
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Boman, J. (1991). Helgason's support theorem for Radon transforms — A new proof and a generalization. In: Herman, G.T., Louis, A.K., Natterer, F. (eds) Mathematical Methods in Tomography. Lecture Notes in Mathematics, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084503
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DOI: https://doi.org/10.1007/BFb0084503
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