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Volumn , Issue 163, 2007, Pages 255-285

Dispersive estimates for schrödinger operators: A survey

(1)  Schlag, W a  

a NONE

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EID: 34248593290     PISSN: 00662313     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Conference Paper
Times cited : (151)

References (89)
  • 1
    • 33845362906 scopus 로고
    • Spectral properties of Schrödinger operators and scattering theory
    • Agmon, S. Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), no. 2, 151-218.
    • (1975) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.2 , Issue.2 , pp. 151-218
    • Agmon, S.1
  • 3
    • 84990553776 scopus 로고
    • Brownian motion and Harnack inequality for Schrödinger operators
    • Aizenman, M., Simon, B. Brownian motion and Harnack inequality for Schrödinger operators. Comm. Pure Appl. Math. 35 (1982), no. 2, 209-273.
    • (1982) Comm. Pure Appl. Math , vol.35 , Issue.2 , pp. 209-273
    • Aizenman, M.1    Simon, B.2
  • 4
    • 0040275794 scopus 로고    scopus 로고
    • p-continuity of wave operators for one dimensional Schrödinger operators
    • p-continuity of wave operators for one dimensional Schrödinger operators. J. Math. Sci. Univ. Tokyo 7 (2000), no. 2, 221-240.
    • (2000) J. Math. Sci. Univ. Tokyo , vol.7 , Issue.2 , pp. 221-240
    • Artbazar, G.1    Yajima, K.2
  • 5
    • 0023306114 scopus 로고
    • Scattering theory for one-dimensional systems with ∫ dx V(x) = 0
    • Bollé, D., Danneels, C., Gesztesy, F. Scattering theory for one-dimensional systems with ∫ dx V(x) = 0. J. Math. Anal. Appl. 122 (1987), no. 2, 496-518.
    • (1987) J. Math. Anal. Appl , vol.122 , Issue.2 , pp. 496-518
    • Bollé, D.1    Danneels, C.2    Gesztesy, F.3
  • 7
    • 0001831351 scopus 로고
    • A complete treatment of low-energy scattering in one dimension
    • Bollé, D., Gesztesy, F., Wilk, S. F. A complete treatment of low-energy scattering in one dimension. J. Operator Theory 13 (1985), no. 1, 3-31.
    • (1985) J. Operator Theory , vol.13 , Issue.1 , pp. 3-31
    • Bollé, D.1    Gesztesy, F.2    Wilk, S.F.3
  • 8
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations
    • Bourgain, J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3 (1993), no. 2, 107-156.
    • (1993) Geom. Funct. Anal , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 9
    • 0033247272 scopus 로고    scopus 로고
    • Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential
    • Bourgain, J. Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential. Comm. Math. Phys. 204 (1999), no. 1, 207-247.
    • (1999) Comm. Math. Phys , vol.204 , Issue.1 , pp. 207-247
    • Bourgain, J.1
  • 10
    • 0033482660 scopus 로고    scopus 로고
    • On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
    • Bourgain, J. On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential. J. Anal. Math. 77 (1999), 315-348.
    • (1999) J. Anal. Math , vol.77 , pp. 315-348
    • Bourgain, J.1
  • 11
    • 0003230767 scopus 로고    scopus 로고
    • Global solutions of nonlinear Schrödinger equations
    • American Mathematical Society, Providence, RI
    • Bourgain, J. Global solutions of nonlinear Schrödinger equations. American Mathematical Society Colloquium Publications, 46. American Mathematical Society, Providence, RI, 1999.
    • (1999) American Mathematical Society Colloquium Publications, 46
    • Bourgain, J.1
  • 12
    • 2942564358 scopus 로고    scopus 로고
    • Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
    • Burq, N., Gerard, P., Tzvetkov, N. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Amer. J. Math. 126 (2004), no. 3, 569-605.
    • (2004) Amer. J. Math , vol.126 , Issue.3 , pp. 569-605
    • Burq, N.1    Gerard, P.2    Tzvetkov, N.3
  • 13
    • 0141503424 scopus 로고    scopus 로고
    • Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
    • Burq, N., Planchon, F., Stalker, J., Tahvildar-Zadeh, A. S. Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. J. Funct. Anal. 203 (2003), no. 2, 519-549.
    • (2003) J. Funct. Anal , vol.203 , Issue.2 , pp. 519-549
    • Burq, N.1    Planchon, F.2    Stalker, J.3    Tahvildar-Zadeh, A.S.4
  • 14
    • 12744280057 scopus 로고    scopus 로고
    • Strichartz estimates for the Wave and Schrödinger Equations with Potentials of Critical Decay
    • Burq, N., Planchon, F., Stalker, J., Tahvildar-Zadeh, A. S. Strichartz estimates for the Wave and Schrödinger Equations with Potentials of Critical Decay, Indiana Univ. Math. J., 53 (2004), no. 6, 1665-1680.
    • (2004) Indiana Univ. Math. J , vol.53 , Issue.6 , pp. 1665-1680
    • Burq, N.1    Planchon, F.2    Stalker, J.3    Tahvildar-Zadeh, A.S.4
  • 15
    • 0002189021 scopus 로고
    • Scattering for the nonlinear Schrödinger equation: States that are close to a soliton. (Russian)
    • Buslaev, V. S., Perelman, G. S. Scattering for the nonlinear Schrödinger equation: States that are close to a soliton. (Russian) Algebra i Analiz 4 (1992), no. 6, 63-102;
    • (1992) Algebra i Analiz , vol.4 , Issue.6 , pp. 63-102
    • Buslaev, V.S.1    Perelman, G.S.2
  • 16
    • 34248566348 scopus 로고    scopus 로고
    • translation in St. Petersburg Math. J. 4 (1993), no. 6, 1111-1142.
    • translation in St. Petersburg Math. J. 4 (1993), no. 6, 1111-1142.
  • 17
    • 34248511665 scopus 로고    scopus 로고
    • Cai, K. Fine properties of charge transfer models, preprint 2003, to appear in Comm. PDE.
    • Cai, K. Fine properties of charge transfer models, preprint 2003, to appear in Comm. PDE.
  • 19
    • 4344573020 scopus 로고    scopus 로고
    • Time asymptotics of the Schrödinger wave function in time-periodic potentials
    • Costin, O., Costin, R. D., Lebowitz, J. L. Time asymptotics of the Schrödinger wave function in time-periodic potentials. J. Statist. Phys. 116 (2004), no. 1-4, 283-310.
    • (2004) J. Statist. Phys , vol.116 , Issue.1-4 , pp. 283-310
    • Costin, O.1    Costin, R.D.2    Lebowitz, J.L.3
  • 20
    • 0037175029 scopus 로고    scopus 로고
    • Decay versus survival of a localized state subjected to harmonic forcing: Exact results
    • Costin, O., Lebowitz, J. L., Rokhlenko, A. Decay versus survival of a localized state subjected to harmonic forcing: Exact results. J. Phys. A 35 (2002), no. 42, 8943-8951.
    • (2002) J. Phys. A , vol.35 , Issue.42 , pp. 8943-8951
    • Costin, O.1    Lebowitz, J.L.2    Rokhlenko, A.3
  • 21
    • 0034355028 scopus 로고    scopus 로고
    • On the wave equation with a potential
    • Cuccagna, S. On the wave equation with a potential. Comm. Partial Differential Equations 25 (2000), no. 7-8, 1549-1565.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.7-8 , pp. 1549-1565
    • Cuccagna, S.1
  • 22
    • 0035595894 scopus 로고    scopus 로고
    • Stabilization of solutions to nonlinear Schrödinger equations
    • Cuccagna, S. Stabilization of solutions to nonlinear Schrödinger equations. Comm. Pure Appl. Math. 54 (2001), no. 9, 1110-1145.
    • (2001) Comm. Pure Appl. Math , vol.54 , Issue.9 , pp. 1110-1145
    • Cuccagna, S.1
  • 23
    • 24344446431 scopus 로고    scopus 로고
    • On the wave equation with a large rough potential
    • D' Ancona, P., Pierfelice, V. On the wave equation with a large rough potential, J. Funct. Anal. 227 (2005), no. 1, 30-77.
    • (2005) J. Funct. Anal , vol.227 , Issue.1 , pp. 30-77
    • D' Ancona, P.1    Pierfelice, V.2
  • 25
    • 1542743771 scopus 로고
    • Time-dependent scattering theory
    • Davies, E. B. Time-dependent scattering theory. Math. Ann. 210 (1974), 149-162.
    • (1974) Math. Ann , vol.210 , pp. 149-162
    • Davies, E.B.1
  • 26
    • 84980148411 scopus 로고
    • Inverse scattering on the line
    • Deift, P., Trubowitz, E. Inverse scattering on the line. Comm. Pure Appl. Math. XXXII (1979), 121-251.
    • (1979) Comm. Pure Appl. Math , vol.32 , pp. 121-251
    • Deift, P.1    Trubowitz, E.2
  • 27
    • 0003155025 scopus 로고    scopus 로고
    • Smoothing effects of Schrödinger evolution groups on Riemannian manifolds
    • Doi, S. Smoothing effects of Schrödinger evolution groups on Riemannian manifolds. Duke Math. J. 82 (1996), no. 3, 679-706.
    • (1996) Duke Math. J , vol.82 , Issue.3 , pp. 679-706
    • Doi, S.1
  • 28
    • 0242473185 scopus 로고    scopus 로고
    • Energy growth in Schrödinger's equation with Markovian forcing
    • Erdogan, M. B., Killip, R., Schlag, W. Energy growth in Schrödinger's equation with Markovian forcing. Comm. Math. Phys. 240 (2003), no. 1-2, 1-29.
    • (2003) Comm. Math. Phys , vol.240 , Issue.1-2 , pp. 1-29
    • Erdogan, M.B.1    Killip, R.2    Schlag, W.3
  • 29
    • 24144498202 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three
    • Erdogan, B., Schlag, W. Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three, Dynamics of PDE 1 (2004), 359-379.
    • (2004) Dynamics of PDE , vol.1 , pp. 359-379
    • Erdogan, B.1    Schlag, W.2
  • 31
    • 4344694217 scopus 로고    scopus 로고
    • Local time-decay of solutions to Schrödinger equations with time-periodic potentials
    • Galtbayar, A., Jensen, A., Yajima, K. Local time-decay of solutions to Schrödinger equations with time-periodic potentials. J. Statist. Phys. 116 (2004), no. 1-4, 231-282.
    • (2004) J. Statist. Phys , vol.116 , Issue.1-4 , pp. 231-282
    • Galtbayar, A.1    Jensen, A.2    Yajima, K.3
  • 32
    • 0141596151 scopus 로고    scopus 로고
    • Decay estimates for the wave equation with potential
    • Georgiev, V., Visciglia, N. Decay estimates for the wave equation with potential. Comm. Partial Differential Equations 28 (2003), no. 7-8, 1325-1369.
    • (2003) Comm. Partial Differential Equations , vol.28 , Issue.7-8 , pp. 1325-1369
    • Georgiev, V.1    Visciglia, N.2
  • 34
    • 34248569013 scopus 로고    scopus 로고
    • Goldberg, M. Dispersive estimates for the three-dimensional Schrödinger equation with rough potential, preprint 2004, to appear in Amer. J. Math.
    • Goldberg, M. Dispersive estimates for the three-dimensional Schrödinger equation with rough potential, preprint 2004, to appear in Amer. J. Math.
  • 36
    • 7544222374 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in dimensions one and three
    • Goldberg, M., Schlag, W. Dispersive estimates for Schrödinger operators in dimensions one and three. Comm. Math. Phys. 251 (2004), no. 1, 157-178.
    • (2004) Comm. Math. Phys , vol.251 , Issue.1 , pp. 157-178
    • Goldberg, M.1    Schlag, W.2
  • 38
    • 34248566387 scopus 로고    scopus 로고
    • Goldberg, M., Visan, M. A Counterexample to Dispersive Estimates for Schrödinger operators in Higher Dimensions, preprint 2005, to appear in Comm. Math. Phys.
    • Goldberg, M., Visan, M. A Counterexample to Dispersive Estimates for Schrödinger operators in Higher Dimensions, preprint 2005, to appear in Comm. Math. Phys.
  • 39
    • 0000492529 scopus 로고
    • Phase space analysis of the charge transfer model
    • Graf, J. M. Phase space analysis of the charge transfer model. Helv. Physica Acta 63 (1990), 107-138.
    • (1990) Helv. Physica Acta , vol.63 , pp. 107-138
    • Graf, J.M.1
  • 40
    • 17444367698 scopus 로고    scopus 로고
    • A Strichartz inequality for the Schrödinger equation on non-trapping asymptotically conic manifolds
    • Hassell, A., Tao, T., Wunsch, J. A Strichartz inequality for the Schrödinger equation on non-trapping asymptotically conic manifolds, Comm. Partial Differential Equations 30 (2005), no. 1-3, 157-205.
    • (2005) Comm. Partial Differential Equations , vol.30 , Issue.1-3 , pp. 157-205
    • Hassell, A.1    Tao, T.2    Wunsch, J.3
  • 42
    • 1542533664 scopus 로고
    • Born series and scattering by time-dependent potentials
    • Howland, J. S. Born series and scattering by time-dependent potentials. Rocky Mount. J. of Math. 10 (1980), no. 3, 521-531.
    • (1980) Rocky Mount. J. of Math , vol.10 , Issue.3 , pp. 521-531
    • Howland, J.S.1
  • 43
    • 0347723684 scopus 로고
    • Stationary scattering theory for time-dependent Hamiltonians
    • Howland, J. S. Stationary scattering theory for time-dependent Hamiltonians. Math. Ann. 207 (1974), 315-335.
    • (1974) Math. Ann , vol.207 , pp. 315-335
    • Howland, J.S.1
  • 44
    • 0001748527 scopus 로고
    • Scattering theory for Hamiltonians periodic in time
    • Howland, J. S. Scattering theory for Hamiltonians periodic in time. Indiana Univ. Math. J. 28 (1979), no. 3, 471-494.
    • (1979) Indiana Univ. Math. J , vol.28 , Issue.3 , pp. 471-494
    • Howland, J.S.1
  • 45
    • 0347578223 scopus 로고    scopus 로고
    • On the absence of positive eigenvalues of Schrödinger operators with rough potentials
    • Ionescu, A., Jerison, D. On the absence of positive eigenvalues of Schrödinger operators with rough potentials. Geom. Funct. Anal. 13 (2003), 1029-1081.
    • (2003) Geom. Funct. Anal , vol.13 , pp. 1029-1081
    • Ionescu, A.1    Jerison, D.2
  • 46
    • 34248568943 scopus 로고    scopus 로고
    • Ionescu, A., Schlag, W. Agmon-Kato-Kuroda theorems for a large class of perturbations, preprint 2004, to appear in Duke Math. Journal.
    • Ionescu, A., Schlag, W. Agmon-Kato-Kuroda theorems for a large class of perturbations, preprint 2004, to appear in Duke Math. Journal.
  • 47
    • 84972562665 scopus 로고
    • m), m ≥ 5
    • m), m ≥ 5. Duke Math. J. 47 (1980), no. 1, 57-80.
    • (1980) Duke Math. J , vol.47 , Issue.1 , pp. 57-80
    • Jensen, A.1
  • 49
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • Jensen, A., Kato, T. Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46 (1979), no. 3, 583-611.
    • (1979) Duke Math. J , vol.46 , Issue.3 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 50
    • 0035619840 scopus 로고    scopus 로고
    • A unified approach to resolvent expansions at thresholds
    • Jensen, A., Nenciu, G. A unified approach to resolvent expansions at thresholds. Rev. Math. Phys. 13 (2001), no. 6, 717-754.
    • (2001) Rev. Math. Phys , vol.13 , Issue.6 , pp. 717-754
    • Jensen, A.1    Nenciu, G.2
  • 51
    • 0036103535 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two-dimensional Schrödinger operators
    • p-boundedness of wave operators for two-dimensional Schrödinger operators. Comm. Math. Phys. 225 (2002), no. 3, 633-637.
    • (2002) Comm. Math. Phys , vol.225 , Issue.3 , pp. 633-637
    • Jensen, A.1    Yajima, K.2
  • 52
    • 84990619685 scopus 로고
    • Decay estimates for Schrödinger operators
    • Journé, J.-L., Soffer, A., Sogge, C. D. Decay estimates for Schrödinger operators. Comm. Pure Appl. Math. 44 (1991), no. 5, 573-604.
    • (1991) Comm. Pure Appl. Math , vol.44 , Issue.5 , pp. 573-604
    • Journé, J.-L.1    Soffer, A.2    Sogge, C.D.3
  • 53
    • 0000570999 scopus 로고
    • Wave operators and similarity for some non-selfadjoint operators
    • Kato, T. Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162 (1965/1966), 258-279.
    • (1965) Math. Ann , vol.162 , pp. 258-279
    • Kato, T.1
  • 54
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel, M., Tao, T. Endpoint Strichartz estimates. Amer. J. Math. 120 (1998), no. 5, 955-980.
    • (1998) Amer. J. Math , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 55
    • 84972558685 scopus 로고
    • Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
    • Kenig, C., Ruiz, A., Sogge, C. D. Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators. Duke Math. J. 55 (1987), 329-347.
    • (1987) Duke Math. J , vol.55 , pp. 329-347
    • Kenig, C.1    Ruiz, A.2    Sogge, C.D.3
  • 56
    • 34248511664 scopus 로고    scopus 로고
    • Krieger, J., Schlag, W. Stable manifolds for all monic supercritical NLS in one dimension, preprint 2005, to appear in Journal AMS.
    • Krieger, J., Schlag, W. Stable manifolds for all monic supercritical NLS in one dimension, preprint 2005, to appear in Journal AMS.
  • 58
    • 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. Funct. Anal. 49 (1) (1982), 10-56.
    • (1982) J. Funct. Anal , vol.49 , Issue.1 , pp. 10-56
    • Murata, M.1
  • 59
    • 30444460599 scopus 로고    scopus 로고
    • On some Schrödinger and wave equations with time dependent potentials, preprint 2004
    • Naibo, V., Stepanov, A. On some Schrödinger and wave equations with time dependent potentials, preprint 2004. Math. Ann. 334 (2006), p. 325-338.
    • (2006) Math. Ann , vol.334 , pp. 325-338
    • Naibo, V.1    Stepanov, A.2
  • 61
    • 0346283249 scopus 로고    scopus 로고
    • Dispersive estimate for the wave equation with the inverse-square potential
    • Planchon, F., Stalker, J., Tahvildar-Zadeh, A. S. Dispersive estimate for the wave equation with the inverse-square potential. Discrete Contin. Dyn. Syst. 9 (2003), no. 6, 1387-1400.
    • (2003) Discrete Contin. Dyn. Syst , vol.9 , Issue.6 , pp. 1387-1400
    • Planchon, F.1    Stalker, J.2    Tahvildar-Zadeh, A.S.3
  • 63
    • 0039687341 scopus 로고
    • Local decay of scattering solutions to Schrödinger's equation
    • Rauch, J. Local decay of scattering solutions to Schrödinger's equation. Comm. Math. Phys. 61 (1978), no. 2, 149-168.
    • (1978) Comm. Math. Phys , vol.61 , Issue.2 , pp. 149-168
    • Rauch, J.1
  • 65
    • 1542508715 scopus 로고    scopus 로고
    • Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
    • Rodnianski, I., Schlag, W. Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Invent. Math. 155 (2004), 451-513.
    • (2004) Invent. Math , vol.155 , pp. 451-513
    • Rodnianski, I.1    Schlag, W.2
  • 66
    • 11844298384 scopus 로고    scopus 로고
    • Dispersive analysis of charge transfer models
    • Rodnianski, I., Schlag, W., Soffer, A. Dispersive analysis of charge transfer models. Comm. Pure Appl. Math. 58 (2005), no. 2, 149-216.
    • (2005) Comm. Pure Appl. Math , vol.58 , Issue.2 , pp. 149-216
    • Rodnianski, I.1    Schlag, W.2    Soffer, A.3
  • 69
    • 84963014993 scopus 로고
    • On local regularity of Schrödinger equations
    • Ruiz, A., Vega, L. On local regularity of Schrödinger equations. Int. Math. Res. Not. 1993 (1993), 13-27.
    • (1993) Int. Math. Res. Not. 1993 , pp. 13-27
    • Ruiz, A.1    Vega, L.2
  • 70
    • 18844449404 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in dimension two
    • Schlag, W. Dispersive estimates for Schrödinger operators in dimension two, Comm. Math. Phys. 257 (2005), 87-117.
    • (2005) Comm. Math. Phys , vol.257 , pp. 87-117
    • Schlag, W.1
  • 71
    • 34248568881 scopus 로고    scopus 로고
    • Schlag, W. Stable manifolds for orbitally unstable NLS, preprint 2004, to appear in Annals of Math.
    • Schlag, W. Stable manifolds for orbitally unstable NLS, preprint 2004, to appear in Annals of Math.
  • 72
    • 85016600983 scopus 로고    scopus 로고
    • Schrödinger semigroups
    • Simon, B. Schrödinger semigroups. Bull. AMS. vol. 7, 447-526.
    • Bull. AMS , vol.7 , pp. 447-526
    • Simon, B.1
  • 73
    • 0001427886 scopus 로고    scopus 로고
    • Global Strichartz estimates for nontrapping perturbations of the Laplacean
    • Smith, H., Sogge, C. Global Strichartz estimates for nontrapping perturbations of the Laplacean. Comm. Partial Differential Equations 25 (2000), no. 11-12, 2171-2183.
    • (2000) Comm. Partial Differential Equations , vol.25 , Issue.11-12 , pp. 2171-2183
    • Smith, H.1    Sogge, C.2
  • 74
    • 0036383355 scopus 로고    scopus 로고
    • Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
    • Staffilani, G., Tataru, D. Strichartz estimates for a Schrödinger operator with nonsmooth coefficients. Comm. Partial Differential Equations 27 (2002), no. 7-8, 1337-1372.
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.7-8 , pp. 1337-1372
    • Staffilani, G.1    Tataru, D.2
  • 75
    • 3042775722 scopus 로고    scopus 로고
    • Scalar waves on a naked-singularity background
    • Stalker, J., Tavildar-Zadeh, S. Scalar waves on a naked-singularity background, Classical Quantum Gravity 21 (2004), no. 12, 2831-2848.
    • (2004) Classical Quantum Gravity , vol.21 , Issue.12 , pp. 2831-2848
    • Stalker, J.1    Tavildar-Zadeh, S.2
  • 77
    • 1642336432 scopus 로고    scopus 로고
    • An estimate for the number of bound states of the Schrödinger operator in two dimensions
    • Stoiciu, M. An estimate for the number of bound states of the Schrödinger operator in two dimensions. Proc. Amer. Math. Soc. 132 (2004), no. 4, 1143-1151.
    • (2004) Proc. Amer. Math. Soc , vol.132 , Issue.4 , pp. 1143-1151
    • Stoiciu, M.1
  • 78
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz, R. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977), no. 3, 705-714.
    • (1977) Duke Math. J , vol.44 , Issue.3 , pp. 705-714
    • Strichartz, R.1
  • 79
    • 0033235140 scopus 로고    scopus 로고
    • k,p-continuity of the Schrödinger wave operators on the line
    • k,p-continuity of the Schrödinger wave operators on the line. Comm. Math. Phys. 208 (1999), no. 2, 507-520.
    • (1999) Comm. Math. Phys , vol.208 , Issue.2 , pp. 507-520
    • Weder, R.1
  • 80
    • 0034410054 scopus 로고    scopus 로고
    • Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential
    • Weder, R. Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential. J. Math. Anal. Appl. 252 (2000), no. 1, 102-123.
    • (2000) J. Math. Anal. Appl , vol.252 , Issue.1 , pp. 102-123
    • Weder, R.1
  • 81
    • 0002283169 scopus 로고    scopus 로고
    • ṗ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • ṗ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. J. Funct. Anal. 170 (2000), no. 1, 37-68.
    • (2000) J. Funct. Anal , vol.170 , Issue.1 , pp. 37-68
    • Weder, R.1
  • 82
    • 0038685281 scopus 로고    scopus 로고
    • p′ estimate for the Schrödinger equation on the half-line
    • p′ estimate for the Schrödinger equation on the half-line. J. Math. Anal. Appl. 281 (2003), no. 1, 233-243.
    • (2003) J. Math. Anal. Appl , vol.281 , Issue.1 , pp. 233-243
    • Weder, R.1
  • 83
    • 0000477848 scopus 로고
    • A multichannel scattering theory for some time dependent Hamiltonians, charge transfer problem
    • Yajima, K. A multichannel scattering theory for some time dependent Hamiltonians, charge transfer problem. Comm. Math. Phys. 75 (1980), no. 2, 153-178.
    • (1980) Comm. Math. Phys , vol.75 , Issue.2 , pp. 153-178
    • Yajima, K.1
  • 84
    • 84972500780 scopus 로고
    • Scattering theory for Schrödinger equations with potentials periodic in time
    • Yajima, K. Scattering theory for Schrödinger equations with potentials periodic in time. J. Math. Soc. Japan 29 (1977), no. 4, 729-743.
    • (1977) J. Math. Soc. Japan , vol.29 , Issue.4 , pp. 729-743
    • Yajima, K.1
  • 85
    • 84972559697 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators
    • k,p-continuity of wave operators for Schrödinger operators. J. Math. Soc. Japan 47 (1995), no. 3, 551-581.
    • (1995) J. Math. Soc. Japan , vol.47 , Issue.3 , pp. 551-581
    • Yajima, K.1
  • 86
    • 0009037488 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m ≥ 4
    • Spectral and scattering theory Sanda, Dekker, New York
    • k,p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m ≥ 4. Spectral and scattering theory (Sanda, 1992), 287-300, Lecture Notes in Pure and Appl. Math., 161, Dekker, New York, 1994.
    • (1992) Lecture Notes in Pure and Appl. Math , vol.161 , pp. 287-300
    • Yajima, K.1
  • 87
    • 0001604108 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators. III. Even-dimensional cases m ≥ 4
    • k,p-continuity of wave operators for Schrödinger operators. III. Even-dimensional cases m ≥ 4. J. Math. Sci. Univ. Tokyo 2 (1995), no. 2, 311-346.
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , Issue.2 , pp. 311-346
    • Yajima, K.1
  • 88
    • 0033235580 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two-dimensional Schrödinger operators
    • p-boundedness of wave operators for two-dimensional Schrödinger operators. Comm. Math. Phys. 208 (1999), no. 1, 125-152.
    • (1999) Comm. Math. Phys , vol.208 , Issue.1 , pp. 125-152
    • Yajima, K.1
  • 89
    • 24144491045 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger equations with threshold resonance and eigenvalue
    • Yajima, K. Dispersive estimates for Schrödinger equations with threshold resonance and eigenvalue, Comm. Math. Phys. 259 (2005), no. 2, 475-509.
    • (2005) Comm. Math. Phys , vol.259 , Issue.2 , pp. 475-509
    • Yajima, K.1


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