The Calderón Reproducing Formula, Windowed X-Ray Transforms, and Radon Transforms in Lp-Spaces

Journal of Fourier Analysis and Applications

Volumn 4, Issue 2, 1998, Pages 175-197

  Rubin, Boris ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

k plane transforms; Lp spaces; Radon transforms; Wavelets; Windowed X ray transforms

Indexed keywords

EID: 1842665776     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02475988     Document Type: Article

References (28)

1. Berenstein, C.A. and Walnut, D.F. (1994). Local inversion of the Radon transform in even dimensions using wavelets. In Proc. Conf. "75 Years of Radon Transform", Vienna, Austria 1992, Gindikin, S.G. and Michor, P., Eds., International Press, Hong Kong, 45-69.
2. Christ, M. (1984). Estimates for the k-plane transform. Indiana Univ. Math. J., 33, 891-910.
3. Coifman, R.R. and Weiss, G. (1977). Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc., 83, 569-645.
4. Drury, S.W. (1989). A survey of k-plane transform estimates. Contemporary Math. 91, 43-55.
5. Frazier, M., Jawerth, B., and Weiss, G. (1991). Littlewood-Paley theory and the study of function spaces. CBMS Reg. Conf. Ser. in Math., 79, Amer. Math. Soc., Providence, RI.
6. Gonzales, F.B. (1991). On the range of the Radon d-plane transform and its dual. Trans. Amer. Math. Soc., 327, 601-619.
7. Helgason, S. (1980). The Radon Transform. Birkhäuser, Boston.
8. Holschneider, M. (1991). Inverse Radon transforms through inverse wavelet transforms. Inverse Problems, 7, 853-861.
9. Kaiser, G.A. and Streater, R.F. (1992). Windowed Radon transforms, analytic signals, and wave equation. In Wavelets - A Tutorial in Theory and Applications, Chui, C.K., Ed., Academic Press, New York, 399-441.
10. Keinert, F. (1989). Inversion of k-plane transforms and applications in computer tomography. SIAM Rev., 31, 273-289.
11. Mattila, P. (1995). Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, Cambridge.
12. Murenzi, R. (1990). Doctoral Thesis. Louvain la Neuve.
13. Natterer, F. (1986). The Mathematics of Computerized Tomography. Wiley, New York.
14. Oberlin, D.M. and Stein, E.M. (1982). Mapping properties of the Radon transform. Indiana Univ. Math. J., 31, 641-650.
15. Petrov, E.E. (1992). Moment conditions for the k-dimensional Radon transformation. Izv. Vyssh. Uchebn. Zaved. Math., 4, 49-53.
16. Rao, M., Sikić, H., and Song, R. (1994). Application of Carleson's theorem to wavelet inversion. Control and Cybernetics, 23, 761-771.
17. Rubin, B. (1995). On Calderón's reproducing formula. In Signal and Image Representation in Combined Spaces, Zeevi, J. and Coifman, R., Eds., Academic Press, New York.
18. Rubin, B. (1996). Fractional Integrals and Potentials. Addison Wesley Longman, Essex, U.K.
19. Rubin, B. (1995/96). Wavelet Type Representations of Riesz Fractional Derivatives. The Hebrew University of Jerusalem, Preprint No. 12.
20. Rubin, B. (1995/96). Inversion of Radon Transforms Using Wavelet Transforms Generated by Wavelet Measures. Math. Scand., to appear.
21. Rubin, B. (1995/96). Inversion of k-plane transforms via continuous wavelet transforms. J. Math. Anal. Appl., to appear.
22. Saeki, S. (1995). On the reproducing formula of Calderon. J. Fourier Anal. Appl., 2, 15-28.
23. 2-functions. J. Math. Anal. Appl., 51, 539-549.
24. Solmon, D.C. (1979). A note on k-plane integral transforms. J. Math. Anal. Appl., 71, 351-358.
25. Stein, E.M. (1970). Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ.
26. Stein, E.M. (1993). Harmonic Analysis, Real Variable Methods, Orthogonality, and Oscillation Integrals. Princeton University Press, Princeton, NJ.
27. p-estimates for Radon transforms in euclidean and non-euclidean spaces. Duke Math. J., 48, 699-727.
28. Walnut, D. (1992). Applications of Gabor and wavelet expansions to the Radon transform. Probabilistic and Stochastic Methods in Analysis, with Applications, NATO ASI Series, Byrnes, J., et al., Eds., Kluwer Academic Publisher, The Netherlands, 187-205.