Mathematische Zeitschrift

, Volume 195, Issue 3, pp 321–343 | Cite as

Asymptotic formulas for the dual radon transform and applications

  • Donald C. Solmon
Article

Keywords

Asymptotic Formula Dual Radon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    Calderon, A.P., Zygmund, A.: On the existence of certain singular integrals. Acta Math.88, 85–139 (1952)Google Scholar
  2. 2.
    Calderon, A.P., Zygmund, A.: Singular integral operators and differential equations. Am. J. Math.79, 901–921 (1957)Google Scholar
  3. 3.
    Cormack, A.M., Quinto, E.T.: A Radon transform on spheres through the origin inR n and applications to the Darboux Equation. Trans. A.M.S.260, 575–581 (1980)Google Scholar
  4. 4.
    Fuglede, B.: An integral formula. Math. Scand.6, 207–212 (1958)Google Scholar
  5. 5.
    Gonzalez, F.: Radon transforms on Grassmann manifolds. Ph.D. Thesis M.I.T. (1984)Google Scholar
  6. 6.
    Helgason, S.: The Radon transform on Euclidean spaces, compact two point homogeneous spaces and Grassmann manifolds. Acta Math.113, 153–180 (1965)Google Scholar
  7. 7.
    Helgason, S.: The Radon Transform. Boston: Birkhäuser 1980Google Scholar
  8. 8.
    Hertle, A.: To appear Habilitationsschrift Univ. Mainz (1986)Google Scholar
  9. 9.
    Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd ed. Berlin Heidelberg New York: Springer 1966Google Scholar
  10. 10.
    Miklin, S.G.: Multidimensional singular integrals and integral equations. London: Pergamon Press 1965Google Scholar
  11. 11.
    Oberlin, D.M., Stein, E.M.: Mapping properties of the Radon Transform. Indiana Univ. Math. J.31, 641–650 (1982)Google Scholar
  12. 12.
    Peters, J.V.: The ham sandwich theorem and some related results. Rocky Mt. J. Math.11, 473–482 (1981)Google Scholar
  13. 13.
    Peters, J.V.: A Tauberian theorem for the Radon transform. Houston J. Math.8, 565–574 (1982)Google Scholar
  14. 14.
    Shepp, L.A., Logan, B.F.: The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci.21, 21–43 (1974)Google Scholar
  15. 15.
    Smith, K.T.: Reconstruction formulas in computed tomography. Computed Tomography. Proc. Symp. Appl. Math.27, L.A., Shepp, Ed. Providence, Am. Math. Soc. 1983Google Scholar
  16. 16.
    Smith, K.T., Solmon, D.C.: Lower dimensional integrability ofL 2 functions. J.M.A.A.51, 539–549 (1975)Google Scholar
  17. 17.
    Smith, K.T., Solmon, D.C., Wagner, S.L.: Practical and mathematical aspects of reconstructing objects from radiographs. Bull. A.M.S.83, 1227–1270 (1977)Google Scholar
  18. 18.
    Sobolev, S.L.: Sur un théorème de l'analyse fonctionelle. C.R. Acad. Sci. U.R.S.S.29, 5–9 (1938)Google Scholar
  19. 19.
    Solmon, D.C.: A note onk-plane integral transforms. J.M.A.A.71, 351–358 (1979)Google Scholar
  20. 20.
    Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton: Princeton Univ. Press 1970Google Scholar
  21. 21.
    Stein, E.M., Weiss, G.: Introduction to Fourier analysis on euclidean spaces. Princeton: Princeton Univ. Press 1971Google Scholar
  22. 22.
    Strichartz, R.S.:L p estimates for Radon transforms in Euclidean and non Euclidean spaces. Duke Math. J.48, 699–727 (1981)Google Scholar
  23. 23.
    Zalcman, L.: Uniqueness and non uniqueness for the Radon transform. Bull. London Math. Soc.XIV, 241–245 (1982)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Donald C. Solmon
    • 1
  1. 1.Mathematics DepartmentOregon State UniversityCorvallisUSA

Personalised recommendations