Radon’s problem for some surfaces in $\textbf {R}^ n$
HTML articles powered by AMS MathViewer
- by A. M. Cormack
- Proc. Amer. Math. Soc. 99 (1987), 305-312
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870790-6
- PDF | Request permission
Abstract:
Radon’s problem for a family of curves in ${R^2}$ has been generalized to a family of $(n - 1)$-dimensional surfaces in ${R^n}$. The problem is posed as a set of integral equations. Solutions to these equations are given for paraboloids and cardioids, and for these cases the null spaces and consistency conditions have been found.References
- A. M. Cormack, The Radon transform on a family of curves in the plane, Proc. Amer. Math. Soc. 83 (1981), no. 2, 325–330. MR 624923, DOI 10.1090/S0002-9939-1981-0624923-1
- A. M. Cormack, The Radon transform on a family of curves in the plane. II, Proc. Amer. Math. Soc. 86 (1982), no. 2, 293–298. MR 667292, DOI 10.1090/S0002-9939-1982-0667292-4 —, SIAM-AMS Proceedings, vol. 14, Amer. Math. Soc., Providence, R.I., 1984, pp. 33-39.
- A. M. Cormack and E. T. Quinto, A Radon transform on spheres through the origin in $\textbf {R}^{n}$ and applications to the Darboux equation, Trans. Amer. Math. Soc. 260 (1980), no. 2, 575–581. MR 574800, DOI 10.1090/S0002-9947-1980-0574800-3
- Stanley R. Deans, The Radon transform and some of its applications, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983. MR 709591 A. Erdelyi et al., Higher transcendental functions, vol. 2, McGraw-Hill, New York, 1953. I. S. Gradshteyn and I. M. Ryzhik, Tables of integrals, Academic Press, New York, 1965.
- Donald Ludwig, The Radon transform on euclidean space, Comm. Pure Appl. Math. 19 (1966), 49–81. MR 190652, DOI 10.1002/cpa.3160190207
- Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968
- A. Papoulis, Optical systems, singularity functions, complex Hankel transforms, J. Opt. Soc. Amer. 57 (1967), 207–213. MR 209776, DOI 10.1364/JOSA.57.000207 E. T. Quinto, private communication. I. N. Sneddon, The use of integral transforms, McGraw-Hill, New York, 1972.
- Jet Wimp, Two integral transform pairs involving hypergeometric functions, Proc. Glasgow Math. Assoc. 7 (1965), 42–44 (1965). MR 177138
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 305-312
- MSC: Primary 44A15; Secondary 44A05, 45A05, 92A07
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870790-6
- MathSciNet review: 870790