Extension of separately analytic functions and applications to range characterization of the exponential Radon transform
Ozan Öktem
Annales Polonici Mathematici, Tome 69 (1998), p. 195-213 / Harvested from The Polish Digital Mathematics Library

We consider the problem of characterizing the range of the exponential Radon transform. The proof uses extension properties of separately analytic functions, and we prove a new theorem about extending such functions.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:262737
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     title = {Extension of separately analytic functions and applications to range characterization of the exponential Radon transform},
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     year = {1998},
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Ozan Öktem. Extension of separately analytic functions and applications to range characterization of the exponential Radon transform. Annales Polonici Mathematici, Tome 69 (1998) pp. 195-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p195bwm/

[000] [1] V. Aguilar, L. Ehrenpreis and P. Kuchment, Range conditions for the exponential Radon transform, J. Anal. Math. 68 (1996), 1-13. | Zbl 0858.44002

[001] [2] J. Becker, Continuing analytic sets across n, Math. Ann. 195 (1973), 103-106. | Zbl 0223.32012

[002] [3] S. Bellini, M. Piarentini, C. Cafforio and F. Rocca, Compensation of tissue absorption in emission tomography, IEEE Trans. Acoust. Speech Signal Process. 27 (1979), 213-218.

[003] [4] C. Berenstein and R. Gay, Complex Variables. An Introduction, Grad. Texts in Math. 125, Springer, New York, 1991. | Zbl 0741.30001

[004] [5] P. Kuchment and S. L'vin, Paley-Wiener theorem for exponential Radon transform, Acta Appl. Math. 18 (1990), 251-260. | Zbl 0705.44001

[005] [6] S. L'vin, Data correction and restoration in emission tomography, in: AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry (June 1993), Lectures in Appl. Math. 30, Amer. Math. Soc., 1994, 149-155.

[006] [7] F. Natterer, The Mathematics of Computerized Tomography, Wiley, New York, 1986. | Zbl 0617.92001

[007] [8] O. Öktem, Comparing range characterizations of the exponential Radon transform, Res. Rep. Math. 17, Stockholm University, 1996.

[008] [9] O. Öktem, Extension of separately analytic functions and applications to range characterization of the exponential Radon transform, Res. Rep. Math. 18, Stockholm University, 1996. | Zbl 0927.44001

[009] [10] I. Ponomaryov, Correction of emission tomography data: effects of detector displacement and non-constant sensitivity, Inverse Problems 10 (1995), 1031-1038. | Zbl 0839.65144

[010] [] J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of n, Ann. Polon. Math. 22 (1969), 145-171. | Zbl 0185.15202