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Volumn 208, Issue 2, 1999, Pages 507-520

The Wk,p-continuity of the Schrödinger wave operators on the line

(1)  Weder, Ricardo a  

a NONE

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EID: 0033235140     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050767     Document Type: Article
Times cited : (94)

References (34)
  • 5
    • 0000109642 scopus 로고
    • Properties of the S matrix of the one-dimensional Schrödinger equation
    • 5. Faddeev, L.D.: Properties of the S matrix of the one-dimensional Schrödinger equation: Trudy Math. Inst. Steklov 73, 314-333 (1964)
    • (1964) Trudy Math. Inst. Steklov , vol.73 , pp. 314-333
    • Faddeev, L.D.1
  • 8
    • 0001649173 scopus 로고
    • English translation
    • [English translation J. Soviet Math. 5, 334-396 (1976)]
    • (1976) J. Soviet Math. , vol.5 , pp. 334-396
  • 9
    • 58149363006 scopus 로고
    • Generalized Strichartz inequalities for the wave equation
    • 7. Ginibre, J., Velo G.: Generalized Strichartz inequalities for the wave equation. J. Funct. Analysis 133, 50-68 (1995)
    • (1995) J. Funct. Analysis , vol.133 , pp. 50-68
    • Ginibre, J.1    Velo, G.2
  • 11
    • 0003216788 scopus 로고    scopus 로고
    • Lectures on Nonlinear Hyperbolic Differential Equations
    • Berlin: Springer-Verlag
    • 9. Hörmander, L.: Lectures on Nonlinear Hyperbolic Differential Equations. Mathématiques & Applications 26, Berlin: Springer-Verlag, 1997
    • (1997) Mathématiques & Applications , vol.26
    • Hörmander, L.1
  • 13
    • 84972548457 scopus 로고
    • p-mapping properties of functions of Schrödinger operators and their applications to scattering theory
    • p-mapping properties of functions of Schrödinger operators and their applications to scattering theory. J. Math. Soc. Japan 47, 253-273 (1995)
    • (1995) J. Math. Soc. Japan , vol.47 , pp. 253-273
    • Jensen, A.1    Nakamura, G.2
  • 14
    • 0000818765 scopus 로고
    • Nonlinear Schrödinger equations
    • Holden, H., Jensen, A. (eds.), Berlin: Springer-Verlag
    • 12. Kato, T.: Nonlinear Schrödinger equations. In: Holden, H., Jensen, A. (eds.), Schrödinger Operators. Lecture Notes in Physics 345, Berlin: Springer-Verlag, 1989, pp. 218-263
    • (1989) Schrödinger Operators. Lecture Notes in Physics , vol.345 , pp. 218-263
    • Kato, T.1
  • 15
    • 0000959853 scopus 로고
    • Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line
    • 13. Klaus, M.: Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line. Inverse Problems 4, 505-512 (1988)
    • (1988) Inverse Problems , vol.4 , pp. 505-512
    • Klaus, M.1
  • 17
    • 0000936941 scopus 로고
    • Low energy scattering for medium range potentials
    • 15. Newton, R., G.: Low energy scattering for medium range potentials. J. Math. Phys. 27, 2720-2730 (1986)
    • (1986) J. Math. Phys. , vol.27 , pp. 2720-2730
    • Newton, R.G.1
  • 18
    • 0004072884 scopus 로고
    • Lectures in Nonlinear Evolution Equations. Initial Value Problems
    • Braunschweig-Wiesbaden: F. Vieweg & Son
    • 16. Racke, R.: Lectures in Nonlinear Evolution Equations. Initial Value Problems. Aspects of Mathematics E 19, Braunschweig-Wiesbaden: F. Vieweg & Son, 1992
    • (1992) Aspects of Mathematics E , vol.19
    • Racke, R.1
  • 22
    • 0003353148 scopus 로고
    • Nonlinear Wave Equations
    • Providence, RI: American Mathematical Society
    • 20. Strauss, W.A.: Nonlinear Wave Equations. CBMS-RCSM 73, Providence, RI: American Mathematical Society, 1989
    • (1989) Cbms-rcsm , vol.73
    • Strauss, W.A.1
  • 24
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • 22. Strichartz, R.S.: Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44, 705-714 (1977)
    • (1977) Duke Math. J. , vol.44 , pp. 705-714
    • Strichartz, R.S.1
  • 26
    • 0001872603 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation
    • 24. Weder, R.: Inverse scattering for the nonlinear Schrödinger equation. Commun. Part. Diff. Equations 22, 2089-2103 (1997)
    • (1997) Commun. Part. Diff. Equations , vol.22 , pp. 2089-2103
    • Weder, R.1
  • 27
    • 0008987459 scopus 로고    scopus 로고
    • ṕ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • Preprint
    • ṕ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. Preprint 1998. To appear in J. Funct. Analysis
    • (1998) J. Funct. Analysis
    • Weder, R.1
  • 28
    • 0002260691 scopus 로고
    • Spectral Theory of Ordinary Differential Operators
    • Berlin: Springer-Verlag
    • 26. Weidmann, J.: Spectral Theory of Ordinary Differential Operators. Lecture Notes in Mathematics 1258, Berlin: Springer-Verlag, 1987
    • (1987) Lecture Notes in Mathematics , vol.1258
    • Weidmann, J.1
  • 29
    • 0021538470 scopus 로고
    • Sound Propagation in Stratified Fluids
    • Berlin-Heidelberg-New York: Springer-Verlag
    • 27. Wilcox, C.H.: Sound Propagation in Stratified Fluids. Applied Mathematical Sciences 50, Berlin-Heidelberg-New York: Springer-Verlag, 1984
    • (1984) Applied Mathematical Sciences , vol.50
    • Wilcox, C.H.1
  • 30
    • 0002820736 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators
    • k,p-continuity of wave operators for Schrödinger operators. Proc. Japan Acad. 69, Ser. A. 94-98 (1993)
    • (1993) Proc. Japan Acad. , vol.69 , Issue.SER. A , pp. 94-98
    • Yajima, K.1
  • 31
    • 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, 551-581 (1995)
    • (1995) J. Math. Soc. Japan , vol.47 , pp. 551-581
    • Yajima, K.1
  • 32
    • 0009037488 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m ≥ 4
    • Ikawa, M. (ed.), New York: Dekker
    • k,p-continuity of wave operators for Schrödinger operators. II. Positive potentials in even dimensions m ≥ 4. In: Ikawa, M. (ed.), Spectral and Scattering Theory (Sanda 1992), Lecture Notes in Pure and Applied Mathematics 161, New York: Dekker 1994, pp. 287-300
    • (1994) Spectral and Scattering Theory (Sanda 1992), Lecture Notes in Pure and Applied Mathematics , vol.161 , pp. 287-300
    • Yajima, K.1
  • 33
    • 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, 311-346 (1995)
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , pp. 311-346
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.