메뉴 건너뛰기




Volumn 26, Issue 9-10, 2001, Pages 1721-1738

Recovery of the singularities of a potential from fixed angle scattering data

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0011005848     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100107457     Document Type: Article
Times cited : (48)

References (29)
  • 1
    • 0000815745 scopus 로고
    • Spectral properties of Schrödinger operators and scattering theory
    • Agmon, S. Spectral properties of Schrödinger operators and scattering theory, Annali della Scuola Norm. Sup. di Pisa serie IV, 1975, Vol. 11(2), 151-218.
    • (1975) Annali della Scuola Norm. Sup. di Pisa Serie IV , vol.11 , Issue.2 , pp. 151-218
    • Agmon, S.1
  • 2
    • 0031282013 scopus 로고    scopus 로고
    • Weighted estimates for the Helmholtz equation and some applications
    • Barcelo, J.; Ruiz, A.; Vega, L. Weighted estimates for the Helmholtz equation and some applications, J. Funct. Anal. 1997, 150(2), 356-382.
    • (1997) J. Funct. Anal. , vol.150 , Issue.2 , pp. 356-382
    • Barcelo, J.1    Ruiz, A.2    Vega, L.3
  • 3
    • 84966216588 scopus 로고
    • Scattering by potential using hyperbolic methods
    • Bayliss, A.; li, Y.; Morawetz, C. Scattering by potential using hyperbolic methods. Math. Comp. 1989, 52, 321-328.
    • (1989) Math. Comp. , vol.52 , pp. 321-328
    • Bayliss, A.1    Li, Y.2    Morawetz, C.3
  • 4
    • 0013199052 scopus 로고
    • The inverse backscattering problem in 3 dimension
    • Eskin, G.; Ralston, J. The inverse backscattering problem in 3 dimension, Comm. Math. Phys. 1989, 124, 169-215.
    • (1989) Comm. Math. Phys. , vol.124 , pp. 169-215
    • Eskin, G.1    Ralston, J.2
  • 5
    • 34249929148 scopus 로고
    • Inverse backscattering in two dimensions
    • Eskin, G.; Ralston, J. Inverse backscattering in two dimensions, Comm. Math. Phys. 1991, 138, 451-486.
    • (1991) Comm. Math. Phys. , vol.138 , pp. 451-486
    • Eskin, G.1    Ralston, J.2
  • 7
    • 0040738373 scopus 로고
    • Recovery of singularities of a potential from singularities of the scattering data
    • Greenleaf, A.; Uhlmann, G. Recovery of singularities of a potential from singularities of the scattering data, Comm. Math. Phys. 1993, 157, 549-572.
    • (1993) Comm. Math. Phys. , vol.157 , pp. 549-572
    • Greenleaf, A.1    Uhlmann, G.2
  • 11
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time decay of the wave function
    • Jensen, A.; Kato, T. Spectral properties of Schrödinger operators and time decay of the wave function, Duke Math. J. 1979, 46, 583-611.
    • (1979) Duke Math. J. , vol.46 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 12
    • 0001226256 scopus 로고
    • Unique continuation and absence of positive eigenvalues for Schrödinger operators
    • Jerison, D.; Kenig, C.E. Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 1985, 121, 463-494.
    • (1985) Ann. of Math. , vol.121 , pp. 463-494
    • Jerison, D.1    Kenig, C.E.2
  • 13
    • 84972558685 scopus 로고
    • Uniform Sobolev inequalities and unique continuation for second order constant coefficients differential operators
    • Kenig, C.E.; Ruiz, A.; Sogge, C.D. Uniform Sobolev inequalities and unique continuation for second order constant coefficients differential operators, Duke Math. J. 1987, 55, 329-347.
    • (1987) Duke Math. J. , vol.55 , pp. 329-347
    • Kenig, C.E.1    Ruiz, A.2    Sogge, C.D.3
  • 15
    • 0002087150 scopus 로고
    • Asymptotic expansions in time for solutions of Schrödinger-type equations
    • Murata, M. Asymptotic expansions in time for solutions of Schrödinger-type equations, J. of Func. An. 1982, 49, 10-56.
    • (1982) J. of Func. An. , vol.49 , pp. 10-56
    • Murata, M.1
  • 16
    • 0000426306 scopus 로고
    • Reconstruction from boundary measurements
    • Nachman, A. Reconstruction from boundary measurements, Ann. of Math. 1988, 128, 531-536.
    • (1988) Ann. of Math. , vol.128 , pp. 531-536
    • Nachman, A.1
  • 17
    • 21544442203 scopus 로고    scopus 로고
    • Recovering singularities from backscattering in two dimension
    • To appear
    • Ola, P.; Päivärinta, L.; Serov, V. Recovering singularities from backscattering in two dimension, To appear Comm. PDE.
    • Comm. PDE
    • Ola, P.1    Päivärinta, L.2    Serov, V.3
  • 18
    • 0040713878 scopus 로고    scopus 로고
    • Recovery of singularities of a multidimensional scattering potential
    • Päivärinta, L.; Serov, V. Recovery of singularities of a multidimensional scattering potential, SIAM J. Math. Anal. 1998, 29, 697-711.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 697-711
    • Päivärinta, L.1    Serov, V.2
  • 19
    • 0041118057 scopus 로고
    • Inversion of discontinuities for the Schrödinger equation in three dimensions
    • Päivärinta, L.; Somersalo, E. Inversion of discontinuities for the Schrödinger equation in three dimensions, SIAM J. Math. Anal. 1991, 22, 480-499.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 480-499
    • Päivärinta, L.1    Somersalo, E.2
  • 20
    • 36749107035 scopus 로고
    • Formal solutions of inverse scattering problems
    • Prosser, R.T. Formal solutions of inverse scattering problems, J. Math. Phys. 1982, 23, 2127-2130.
    • (1982) J. Math. Phys. , vol.23 , pp. 2127-2130
    • Prosser, R.T.1
  • 22
    • 84963014993 scopus 로고
    • On local regularity of Schrödinger equations
    • Ruiz, A.; Vega, L. On local regularity of Schrödinger equations, Interna. Math. Res. Notices 1993, 1, 13-27.
    • (1993) Interna. Math. Res. Notices , vol.1 , pp. 13-27
    • Ruiz, A.1    Vega, L.2
  • 23
    • 0000444043 scopus 로고
    • Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces
    • Sawyer, E.; Wheeden, R.L. Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Am. J. of Math. 1992, 114, 813-874.
    • (1992) Am. J. of Math. , vol.114 , pp. 813-874
    • Sawyer, E.1    Wheeden, R.L.2
  • 24
    • 0041118035 scopus 로고
    • On estimates of the resolvent of the Laplace operator over the entire space
    • Serov, V.S. On estimates of the resolvent of the Laplace operator over the entire space, Mat. Zametki 1992, 52(6), 109-118;
    • (1992) Mat. Zametki , vol.52 , Issue.6 , pp. 109-118
    • Serov, V.S.1
  • 25
    • 21544471422 scopus 로고
    • Translation in Math. Notes 1992, 52, n.5-6, 1247-1254.
    • (1992) Translation in Math. Notes , vol.52 , Issue.5-6 , pp. 1247-1254
  • 26
    • 0001420005 scopus 로고
    • Generic uniqueness for two inverse problems in potential scattering
    • Stefanov, P. Generic uniqueness for two inverse problems in potential scattering, Comm. PDE 1992, 17, 55-68.
    • (1992) Comm. PDE , vol.17 , pp. 55-68
    • Stefanov, P.1
  • 27
    • 0346088998 scopus 로고    scopus 로고
    • Inverse backscattering for the acoustic equation
    • Stefanov, P.; Uhlmann, G. Inverse backscattering for the acoustic equation, SIAM J. Math. Anal. 1997, 28, 1191-1204.
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 1191-1204
    • Stefanov, P.1    Uhlmann, G.2
  • 28
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • Sylvester, J.; Uhlmann, G. A global uniqueness theorem for an inverse boundary value problem, Annals of Math. 1987, 125(92), 112.
    • (1987) Annals of Math. , vol.125 , Issue.92 , pp. 112
    • Sylvester, J.1    Uhlmann, G.2
  • 29
    • 84968496791 scopus 로고
    • A restriction theorem for the Fourier transform
    • Tomas, P. A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 1975, 81, 477-478.
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 477-478
    • Tomas, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.