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

Ozan Öktem

Annales Polonici Mathematici (1998)

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

Abstract

top
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.

How to cite

top

Ozan 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. [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. [2] J. Becker, Continuing analytic sets across ℝ n , Math. Ann. 195 (1973), 103-106. Zbl0223.32012
  3. [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. 
  4. [4] C. Berenstein and R. Gay, Complex Variables. An Introduction, Grad. Texts in Math. 125, Springer, New York, 1991. Zbl0741.30001
  5. [5] P. Kuchment and S. L'vin, Paley-Wiener theorem for exponential Radon transform, Acta Appl. Math. 18 (1990), 251-260. Zbl0705.44001
  6. [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. [7] F. Natterer, The Mathematics of Computerized Tomography, Wiley, New York, 1986. Zbl0617.92001
  8. [8] O. Öktem, Comparing range characterizations of the exponential Radon transform, Res. Rep. Math. 17, Stockholm University, 1996. 
  9. [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. [10] I. Ponomaryov, Correction of emission tomography data: effects of detector displacement and non-constant sensitivity, Inverse Problems 10 (1995), 1031-1038. Zbl0839.65144
  11. [] J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of ℂ n , Ann. Polon. Math. 22 (1969), 145-171. Zbl0185.15202

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.