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1998 | 70 | 1 | 195-213

Tytuł artykułu

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

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

70

Numer

1

Strony

195-213

Daty

wydano
1998
otrzymano
1997-11-29
poprawiono
1998-08-17

Twórcy

autor
  • Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden

Bibliografia

  • [1] V. Aguilar, L. Ehrenpreis and P. Kuchment, Range conditions for the exponential Radon transform, J. Anal. Math. 68 (1996), 1-13.
  • [2] J. Becker, Continuing analytic sets across $ℝ^n$, Math. Ann. 195 (1973), 103-106.
  • [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] C. Berenstein and R. Gay, Complex Variables. An Introduction, Grad. Texts in Math. 125, Springer, New York, 1991.
  • [5] P. Kuchment and S. L'vin, Paley-Wiener theorem for exponential Radon transform, Acta Appl. Math. 18 (1990), 251-260.
  • [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.
  • [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.
  • [10] I. Ponomaryov, Correction of emission tomography data: effects of detector displacement and non-constant sensitivity, Inverse Problems 10 (1995), 1031-1038.
  • [] J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $ℂ^n$, Ann. Polon. Math. 22 (1969), 145-171.

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