# Extension of separately analytic functions and applications to range characterization of the exponential Radon transform

Annales Polonici Mathematici (1998)

- Volume: 70, Issue: 1, page 195-213
- ISSN: 0066-2216

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topOzan Öktem. "Extension of separately analytic functions and applications to range characterization of the exponential Radon transform." Annales Polonici Mathematici 70.1 (1998): 195-213. <http://eudml.org/doc/262737>.

@article{OzanÖktem1998,

abstract = {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.},

author = {Ozan Öktem},

journal = {Annales Polonici Mathematici},

keywords = {exponential Radon transform; range characterization; separately analytic functions},

language = {eng},

number = {1},

pages = {195-213},

title = {Extension of separately analytic functions and applications to range characterization of the exponential Radon transform},

url = {http://eudml.org/doc/262737},

volume = {70},

year = {1998},

}

TY - JOUR

AU - Ozan Öktem

TI - Extension of separately analytic functions and applications to range characterization of the exponential Radon transform

JO - Annales Polonici Mathematici

PY - 1998

VL - 70

IS - 1

SP - 195

EP - 213

AB - 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.

LA - eng

KW - exponential Radon transform; range characterization; separately analytic functions

UR - http://eudml.org/doc/262737

ER -

## References

top- [1] V. Aguilar, L. Ehrenpreis and P. Kuchment, Range conditions for the exponential Radon transform, J. Anal. Math. 68 (1996), 1-13. Zbl0858.44002
- [2] J. Becker, Continuing analytic sets across ${\mathbb{R}}^{n}$, Math. Ann. 195 (1973), 103-106. Zbl0223.32012
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- [5] P. Kuchment and S. L'vin, Paley-Wiener theorem for exponential Radon transform, Acta Appl. Math. 18 (1990), 251-260. Zbl0705.44001
- [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.
- [7] F. Natterer, The Mathematics of Computerized Tomography, Wiley, New York, 1986. Zbl0617.92001
- [8] O. Öktem, Comparing range characterizations of the exponential Radon transform, Res. Rep. Math. 17, Stockholm University, 1996.
- [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. Zbl0927.44001
- [10] I. Ponomaryov, Correction of emission tomography data: effects of detector displacement and non-constant sensitivity, Inverse Problems 10 (1995), 1031-1038. Zbl0839.65144
- [] J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of ${\u2102}^{n}$, Ann. Polon. Math. 22 (1969), 145-171. Zbl0185.15202

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