Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Analytic multipliers of the Radon transform


Author: James V. Peters
Journal: Proc. Amer. Math. Soc. 72 (1978), 485-491
MSC: Primary 44A15; Secondary 43A85
DOI: https://doi.org/10.1090/S0002-9939-1978-0509239-6
MathSciNet review: 509239
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define the Radon transform over the real and complex domain, and list some of its simplest properties. For the complex domain $ {{\mathbf{C}}^n}$, a theorem of the Paley-Wiener type is obtained to determine the support of a continuous, integrable function from its Radon transform. The construction requires defining an associated function of the Radon transform for each $ z \in {{\mathbf{C}}^n}$. The support of the function is then obtained via analytic multipliers of the associated functions.


References [Enhancements On Off] (What's this?)

  • [1] I. M. Gel'fand, M. I. Graev and N. Ya Vilenkin, Integral geometry and representation theory, Academic Press, New York, 1966.
  • [2] I. M. Gel'fand and G. E. Shilov, Properties and operations, Academic Press, New York, 1966. MR 0435831 (55:8786a)
  • [3] -, Functions and generalized spaces, Academic Press, New York, 1966.
  • [4] F. John, Plane waves and spherical harmonics, Interscience, New York, 1955. MR 0075429 (17:746d)
  • [5] J. V. Peters, Radon transforms over the real and complex domain, Doctoral Thesis, Stevens Institute of Technology, Hoboken, N. J., 1976.
  • [6] G. E. Shilov, Generalized functions of partial differential equations, Gordon and Breach, New York, 1968. MR 0230129 (37:5694)
  • [7] K. T. Smith, D. C. Solmon and S. L. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs. Bull. Amer. Math. Soc. 83 (1977), 1227-1270. MR 0490032 (58:9394a)
  • [8] D. C. Solmon, A note on K-plane integral transforms, Math. Anal. Appl. (to appear). MR 548770 (80m:44010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 44A15, 43A85

Retrieve articles in all journals with MSC: 44A15, 43A85


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0509239-6
Keywords: Radon transform, support, analytic multipliers
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society