메뉴 건너뛰기




Volumn 29, Issue 3, 1998, Pages 697-711

Recovery of singularities of a multidimensional scattering potential

Author keywords

Born approximation; Inverse problem; Schr dinger scattering

Indexed keywords


EID: 0040713878     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096305796     Document Type: Article
Times cited : (32)

References (14)
  • 1
    • 0039931138 scopus 로고
    • An inverse scattering result for measure potentials
    • R. FORD, An inverse scattering result for measure potentials, Inverse Problems, 11 (1995), pp. 939-948.
    • (1995) Inverse Problems , vol.11 , pp. 939-948
    • Ford, R.1
  • 2
    • 0039931152 scopus 로고    scopus 로고
    • Inverse scattering for the Schrödinger equation in dimension 1 up to smooth functions
    • R. NOVIKOV, Inverse scattering for the Schrödinger equation in dimension 1 up to smooth functions, Bull. Sci. Math., 120 (1996), pp. 473-491.
    • (1996) Bull. Sci. Math. , vol.120 , pp. 473-491
    • Novikov, R.1
  • 3
    • 0041118057 scopus 로고
    • Inversion of discontinuities for the Schrödinger equation in three dimensions
    • L. PÄIVÄRINTA AND E. SOMERSALO, Inversion of discontinuities for the Schrödinger equation in three dimensions, SIAM J. Math. Anal., 22 (1991), pp. 480-499.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 480-499
    • Päivärinta, L.1    Somersalo, E.2
  • 4
    • 0010968912 scopus 로고
    • Reconstruction of singularities of a scattering potential in two dimensions
    • L. PÄIVÄRINTA, V.S. SEROV, AND E. SOMERSALO, Reconstruction of singularities of a scattering potential in two dimensions, Adv. Appl. Maths., 15 (1994), pp. 97-113.
    • (1994) Adv. Appl. Maths. , vol.15 , pp. 97-113
    • Päivärinta, L.1    Serov, V.S.2    Somersalo, E.3
  • 5
    • 0041118035 scopus 로고
    • On estimates of the resolvent of the Laplace operator over the entire space
    • V.S. SEROV, On estimates of the resolvent of the Laplace operator over the entire space, Mat. Zametki, 52 (1992), pp. 109-118.
    • (1992) Mat. Zametki , vol.52 , pp. 109-118
    • Serov, V.S.1
  • 6
    • 0040523946 scopus 로고
    • One-dimensional electromagnetic inverse reflection problem: Formulation as a Riemann-Hilbert problem and imaging of discontinuities
    • E. SOMERSALO, One-dimensional electromagnetic inverse reflection problem: Formulation as a Riemann-Hilbert problem and imaging of discontinuities, SIAM J. Appl. Math., 49 (1989), pp. 944-951.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 944-951
    • Somersalo, E.1
  • 7
    • 84972581809 scopus 로고
    • Some, properties of the scattering amplitude and inverse scattering problem
    • Y. SAITO, Some, properties of the scattering amplitude and inverse scattering problem, Osaka J. Maths., 19 (1982), pp. 527-547.
    • (1982) Osaka J. Maths. , vol.19 , pp. 527-547
    • Saito, Y.1
  • 8
    • 33645661574 scopus 로고
    • On recovering the potential in the Schrödinger operator on the line using Born's approximation
    • V.S. SEROV AND D.S. TKACHENKO, On recovering the potential in the Schrödinger operator on the line using Born's approximation, Differentsial'nye Uravneniya, 29 (1993), pp. 108-116.
    • (1993) Differentsial'nye Uravneniya , vol.29 , pp. 108-116
    • Serov, V.S.1    Tkachenko, D.S.2
  • 10
    • 0040738373 scopus 로고
    • Recovering singularities of a potential from singularities of scattering data
    • A. GREENLEAF AND G. UHLMANN, Recovering singularities of a potential from singularities of scattering data, Comm. Math. Phys., 157 (1993), pp. 549-572.
    • (1993) Comm. Math. Phys. , vol.157 , pp. 549-572
    • Greenleaf, A.1    Uhlmann, G.2
  • 11
    • 84968503470 scopus 로고
    • Inverse scattering for singular potentials in two dimensions
    • Z. SUN AND G. UHLMANN, Inverse scattering for singular potentials in two dimensions, Trans. Amer. Math. Soc., 338 (1993), pp. 363-374.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 363-374
    • Sun, Z.1    Uhlmann, G.2
  • 12
    • 21144461533 scopus 로고
    • Recovery of singularities for formally determined inverse problems
    • Z. SUN AND G. UHLMANN, Recovery of singularities for formally determined inverse problems, Comm. Math. Phys., 153 (1993), pp. 431-445.
    • (1993) Comm. Math. Phys. , vol.153 , pp. 431-445
    • Sun, Z.1    Uhlmann, G.2
  • 13
    • 0004058897 scopus 로고
    • Akademische Verlagsgeschellchaft Geest and Portig K.-G., Leipzig, Germany
    • H. TRIEBEL, Theory of Function Spaces, Akademische Verlagsgeschellchaft Geest and Portig K.-G., Leipzig, Germany, 1983.
    • (1983) Theory of Function Spaces
    • Triebel, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.