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.
@article{bwmeta1.element.bwnjournal-article-apmv70z1p195bwm, author = {Ozan \"Oktem}, title = {Extension of separately analytic functions and applications to range characterization of the exponential Radon transform}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {195-213}, zbl = {0927.44001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p195bwm} }
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 , 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 , Ann. Polon. Math. 22 (1969), 145-171. | Zbl 0185.15202