메뉴 건너뛰기




Volumn 35, Issue 4, 2001, Pages 270-283

The Generalized Radon Transform on the Plane, the Inverse Transform, and the Cavalieri Conditions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035566110     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013126507543     Document Type: Article
Times cited : (9)

References (38)
  • 3
    • 0004070324 scopus 로고
    • Birkhäuser, Boston-Basel-Stuttgart
    • S. Helgason, The Radon Transform, Birkhäuser, Boston-Basel-Stuttgart, 1980.
    • (1980) The Radon Transform
    • Helgason, S.1
  • 6
    • 0041017376 scopus 로고
    • On some results of Gelfand in integral geometry
    • Pseudodifferential operators and Applications Notre Dame, Ind., Providence, R.I
    • V. Guillemin, "On some results of Gelfand in integral geometry," In: Pseudodifferential operators and Applications (Notre Dame, Ind., 1984), Proc. Sympos. Pure Math., Vol. 43, Providence, R.I., 1985, pp. 149-155.
    • (1984) Proc. Sympos. Pure Math. , vol.43 , pp. 149-155
    • Guillemin, V.1
  • 8
    • 84968521990 scopus 로고
    • The dependence of the generalized Radon transform on defining measures
    • E. T. Quinto, "The dependence of the generalized Radon transform on defining measures," Trans. Amer. Math. Soc., 257, No. 2, 331-346 (1980).
    • (1980) Trans. Amer. Math. Soc. , vol.257 , Issue.2 , pp. 331-346
    • Quinto, E.T.1
  • 9
    • 84972563437 scopus 로고
    • Nonlocal inversion formulas for the X-ray transformation
    • A. Greenleaf and G. Uhlmann, "Nonlocal inversion formulas for the X-ray transformation," Duke Math. J., 58, No. 1, 205-240 (1989).
    • (1989) Duke Math. J. , vol.58 , Issue.1 , pp. 205-240
    • Greenleaf, A.1    Uhlmann, G.2
  • 11
    • 0002276411 scopus 로고
    • Regularity of Fourier integral operators
    • Zurich, Birkhauser, Basel
    • D. H. Phong, "Regularity of Fourier integral operators," In: Proc. Intern. Congress of Math., Zurich, 1994, Vol. 2, Birkhauser, Basel, 1995, pp. 862-874.
    • (1994) Proc. Intern. Congress of Math. , vol.2 , pp. 862-874
    • Phong, D.H.1
  • 12
    • 84972570733 scopus 로고
    • Singular Radon transforms and oscillatory integrals
    • D. H. Phong and E. M. Stein, "Singular Radon transforms and oscillatory integrals," Duke Math. J., 58, No. 2, 347-369 (1989).
    • (1989) Duke Math. J. , vol.58 , Issue.2 , pp. 347-369
    • Phong, D.H.1    Stein, E.M.2
  • 13
    • 0011634465 scopus 로고
    • Radon transforms on curves in the plane
    • Tomography, Impedance Imaging, and Integral Geometry, Amer. Math. Soc., Providence, R.I
    • E. T. Quinto, "Radon transforms on curves in the plane," In: Tomography, Impedance Imaging, and Integral Geometry, Lectures in Appl. Math., Vol. 30, Amer. Math. Soc., Providence, R.I., 1994, pp. 231-244.
    • (1994) Lectures in Appl. Math. , vol.30 , pp. 231-244
    • Quinto, E.T.1
  • 14
    • 84972575357 scopus 로고
    • Support theorems for real-analytical Radon transforms
    • J. Boman and E. T. Quinto, "Support theorems for real-analytical Radon transforms," Duke Math. J., 55, No. 4, 943-948 (1987).
    • (1987) Duke Math. J. , vol.55 , Issue.4 , pp. 943-948
    • Boman, J.1    Quinto, E.T.2
  • 15
    • 0030213465 scopus 로고    scopus 로고
    • Injectivity sets for the Radon transform over circles and complete systems of radial functions
    • M. L. Agranovsky and E. T. Quinto, "Injectivity sets for the Radon transform over circles and complete systems of radial functions," J. Funct. Anal., 139, 383-414 (1996).
    • (1996) J. Funct. Anal. , vol.139 , pp. 383-414
    • Agranovsky, M.L.1    Quinto, E.T.2
  • 16
    • 0000731375 scopus 로고
    • Estimates for singular Radon transforms and pseudodifferential operators with singular symbols
    • A. Greenleaf and G. Uhlmann, "Estimates for singular Radon transforms and pseudodifferential operators with singular symbols," J. Funct. Anal., 89, 202-239 (1990).
    • (1990) J. Funct. Anal. , vol.89 , pp. 202-239
    • Greenleaf, A.1    Uhlmann, G.2
  • 17
    • 38249004974 scopus 로고
    • Sobolev estimates for singular Radon transforms
    • A. A. Thomson, "Sobolev estimates for singular Radon transforms," J. Funct. Anal., 112, 61-96 (1993).
    • (1993) J. Funct. Anal. , vol.112 , pp. 61-96
    • Thomson, A.A.1
  • 21
    • 0043247742 scopus 로고
    • Reconstructing functions from integrals over a family of curves
    • V. G. Romanov, "Reconstructing functions from integrals over a family of curves," Sib. Mat. Zh., 7, No. 5, 1206-1208 (1967).
    • (1967) Sib. Mat. Zh. , vol.7 , Issue.5 , pp. 1206-1208
    • Romanov, V.G.1
  • 22
    • 84966210499 scopus 로고
    • Radon transform on a family of curves in the plane
    • A. M. Cormack, "Radon transform on a family of curves in the plane," I, Proc. Amer. Math. Soc., 83, 325-330 (1981); II, ibid., 86, 293-298 (1982).
    • (1981) I, Proc. Amer. Math. Soc. , vol.83 , pp. 325-330
    • Cormack, A.M.1
  • 23
    • 84966205073 scopus 로고
    • A. M. Cormack, "Radon transform on a family of curves in the plane," I, Proc. Amer. Math. Soc., 83, 325-330 (1981); II, ibid., 86, 293-298 (1982).
    • (1982) II, Proc. Amer. Math. Soc. , vol.86 , pp. 293-298
  • 24
    • 84980148285 scopus 로고
    • The Paley-Wiener theorem for the Radon transform
    • P. D. Lax and P. S. Phillips, "The Paley-Wiener theorem for the Radon transform," Comm. Pure Appl. Math., 23, No. 3, 409-424 (1970).
    • (1970) Comm. Pure Appl. Math. , vol.23 , Issue.3 , pp. 409-424
    • Lax, P.D.1    Phillips, P.S.2
  • 26
    • 0042245448 scopus 로고
    • On the solvability of a problem in integral geometry
    • Yu. E. Anikinov, "On the solvability of a problem in integral geometry," Mat. Sb., 101 (143), No. 2, 271-279 (1976).
    • (1976) Mat. Sb. , vol.101-143 , Issue.2 , pp. 271-279
    • Anikinov, Y.E.1
  • 27
    • 0001905162 scopus 로고
    • The problem of reconstructing the two-dimensional Riemannian metric and integral geometry
    • R. G. Mukhometov, "The problem of reconstructing the two-dimensional Riemannian metric and integral geometry," Dokl. Akad. Nauk SSSR, 232, No. 1, 32-35 (1977).
    • (1977) Dokl. Akad. Nauk SSSR , vol.232 , Issue.1 , pp. 32-35
    • Mukhometov, R.G.1
  • 29
    • 0016027865 scopus 로고
    • On the reconstruction of a function on a circular domain from a sampling of its line integrals
    • R. B. Marr, "On the reconstruction of a function on a circular domain from a sampling of its line integrals," J. Math. Anal. Appl., 45, 357-374 (1974).
    • (1974) J. Math. Anal. Appl. , vol.45 , pp. 357-374
    • Marr, R.B.1
  • 32
    • 0010207359 scopus 로고    scopus 로고
    • Estimates with constants for a class of oscillating integrals
    • D. A. Popov, "Estimates with constants for a class of oscillating integrals," Usp. Mat. Nauk, 52, No. 1, 77-148 (1997).
    • (1997) Usp. Mat. Nauk , vol.52 , Issue.1 , pp. 77-148
    • Popov, D.A.1
  • 34
    • 33646945324 scopus 로고
    • The spectral function of elliptic operator
    • L. Hörmander, "The spectral function of elliptic operator," Acta Math., 121, Nos. 3-4, 193-218 (1968).
    • (1968) Acta Math. , vol.121 , Issue.3-4 , pp. 193-218
    • Hörmander, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.