메뉴 건너뛰기




Volumn 258, Issue 3, 2010, Pages 933-955

High-frequency propagation for the Schrödinger equation on the torus

Author keywords

Quantum limits; Resonances; Schr dinger equation on the torus; Semiclassical (Wigner) measures; Strichartz estimates; Two microlocal Wigner measures

Indexed keywords


EID: 70449120733     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2009.09.020     Document Type: Article
Times cited : (51)

References (20)
  • 1
    • 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 2 (1993) 107-156
    • (1993) Geom. Funct. Anal. , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 2
    • 84963018923 scopus 로고
    • Eigenfunction bounds for the Laplacian on the n-torus
    • Bourgain J. Eigenfunction bounds for the Laplacian on the n-torus. Int. Math. Res. Not. 3 (1993) 61-66
    • (1993) Int. Math. Res. Not. , vol.3 , pp. 61-66
    • Bourgain, J.1
  • 3
    • 0003230767 scopus 로고    scopus 로고
    • Global Solutions of Nonlinear Schrödinger Equations
    • American Mathematical Society, Providence, RI
    • Bourgain J. Global Solutions of Nonlinear Schrödinger Equations. Amer. Math. Soc. Colloq. Publ. vol. 46 (1999), American Mathematical Society, Providence, RI
    • (1999) Amer. Math. Soc. Colloq. Publ. , vol.46
    • Bourgain, J.1
  • 4
    • 2942564358 scopus 로고    scopus 로고
    • Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
    • Burq N., Gérard P., and Tzvetkov N. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Amer. J. Math. 126 3 (2004) 569-605
    • (2004) Amer. J. Math. , vol.126 , Issue.3 , pp. 569-605
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 5
    • 12144282712 scopus 로고    scopus 로고
    • Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
    • Burq N., Gérard P., and Tzvetkov N. Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Invent. Math. 159 1 (2005) 187-223
    • (2005) Invent. Math. , vol.159 , Issue.1 , pp. 187-223
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 6
    • 20444425674 scopus 로고    scopus 로고
    • Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations
    • Burq N., Gérard P., and Tzvetkov N. Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Ann. Sci. École Norm. Sup. (4) 38 2 (2005) 255-301
    • (2005) Ann. Sci. École Norm. Sup. (4) , vol.38 , Issue.2 , pp. 255-301
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 8
    • 0041724636 scopus 로고    scopus 로고
    • Propagation and absorption of concentration effects near shock hypersurfaces for the heat equation
    • Fermanian-Kammerer C. Propagation and absorption of concentration effects near shock hypersurfaces for the heat equation. Asymptot. Anal. 24 2 (2000) 107-141
    • (2000) Asymptot. Anal. , vol.24 , Issue.2 , pp. 107-141
    • Fermanian-Kammerer, C.1
  • 9
    • 0013386103 scopus 로고    scopus 로고
    • Mesures semi-classiques et croisement de modes
    • Fermanian-Kammerer C., and Gérard P. Mesures semi-classiques et croisement de modes. Bull. Soc. Math. France 130 1 (2002) 123-168
    • (2002) Bull. Soc. Math. France , vol.130 , Issue.1 , pp. 123-168
    • Fermanian-Kammerer, C.1    Gérard, P.2
  • 10
    • 0003332429 scopus 로고
    • Harmonic Analysis in Phase Space
    • Princeton University Press, Princeton, NJ
    • Folland G.B. Harmonic Analysis in Phase Space. Ann. of Math. Stud. vol. 122 (1989), Princeton University Press, Princeton, NJ
    • (1989) Ann. of Math. Stud. , vol.122
    • Folland, G.B.1
  • 12
    • 70449111452 scopus 로고    scopus 로고
    • P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire sur les Équations aux Dérivées Partielles, 1990-1991, Exp. No. XVI, Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 1991
    • P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire sur les Équations aux Dérivées Partielles, 1990-1991, Exp. No. XVI, Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 1991
  • 13
    • 84973997812 scopus 로고
    • Ergodic properties of eigenfunctions for the Dirichlet problem
    • Gérard P., and Leichtnam E. Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J. 71 2 (1993) 559-607
    • (1993) Duke Math. J. , vol.71 , Issue.2 , pp. 559-607
    • Gérard, P.1    Leichtnam, E.2
  • 15
    • 0345810412 scopus 로고    scopus 로고
    • Quantum limits on flat tori
    • Jakobson D. Quantum limits on flat tori. Ann. of Math. 145 2 (1997) 235-266
    • (1997) Ann. of Math. , vol.145 , Issue.2 , pp. 235-266
    • Jakobson, D.1
  • 17
    • 67650721205 scopus 로고    scopus 로고
    • Semiclassical measures and the Schrödinger flow on Riemannian manifolds
    • Macià F. Semiclassical measures and the Schrödinger flow on Riemannian manifolds. Nonlinearity 22 (2009) 1003-1020
    • (2009) Nonlinearity , vol.22 , pp. 1003-1020
    • Macià, F.1
  • 19
    • 0001485147 scopus 로고    scopus 로고
    • A semi-classical picture of quantum scattering
    • Nier F. A semi-classical picture of quantum scattering. Ann. Sci. École Norm. Sup. (4) 29 2 (1996) 149-183
    • (1996) Ann. Sci. École Norm. Sup. (4) , vol.29 , Issue.2 , pp. 149-183
    • Nier, F.1
  • 20
    • 0000855641 scopus 로고
    • On Fourier coefficients and transforms of functions of two variables
    • Zygmund A. On Fourier coefficients and transforms of functions of two variables. Studia Math. 50 (1974) 189-201
    • (1974) Studia Math. , vol.50 , pp. 189-201
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.