On the scattering matrix for perturbations of constant sign

D. R. Yafaev

Annales de l'I.H.P. Physique théorique (1992)

  • Volume: 57, Issue: 4, page 361-384
  • ISSN: 0246-0211

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Yafaev, D. R.. "On the scattering matrix for perturbations of constant sign." Annales de l'I.H.P. Physique théorique 57.4 (1992): 361-384. <http://eudml.org/doc/76591>.

@article{Yafaev1992,
author = {Yafaev, D. R.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {spectral theory for perturbation of unitary operators; scattering theory; time-independent representation of the scattering matrix; Schrödinger operators; spectrum of unitary scattering matrices},
language = {eng},
number = {4},
pages = {361-384},
publisher = {Gauthier-Villars},
title = {On the scattering matrix for perturbations of constant sign},
url = {http://eudml.org/doc/76591},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Yafaev, D. R.
TI - On the scattering matrix for perturbations of constant sign
JO - Annales de l'I.H.P. Physique théorique
PY - 1992
PB - Gauthier-Villars
VL - 57
IS - 4
SP - 361
EP - 384
LA - eng
KW - spectral theory for perturbation of unitary operators; scattering theory; time-independent representation of the scattering matrix; Schrödinger operators; spectrum of unitary scattering matrices
UR - http://eudml.org/doc/76591
ER -

References

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  1. [1] M.Sh. Birman and M.G. Krein, On the Theory of Wave Operators and Scattering Operators, Dokl. Acad. Nauk. U.S.S.R., T. 144, 1962, pp. 475-478 (Russian). Zbl0196.45004MR139007
  2. [2] M.Sh. Birman and M.G. Krein, Some Problems of the Theory of Wave Operators and Scattering Operators, Proc. of the joint Sov.-Amer. Symp on Partial Diff. Equations, Novosibirsk, 1963 (Russian). 
  3. [3] L.S. Koplienko, On the Spectrum of the Scattering Matrix, Izv. VUZov, Math., No. 5, 1971, pp. 54-61 (Russian). MR290176
  4. [4] S.J. Rotfeld, On Spectral Properties of the Scattering Matrix, II, Topics in Math. Phys., Leningrad Univ, T. 7, 1974, pp. 135-149 (Russian). MR445312
  5. [5] L. Landau et E. Lifshitz, Mécanique Quantique. Théorie non relativiste, Moscou, MIR, 1967. Zbl0144.47605
  6. [6] S.T. Kuroda, Some Remarks on Scattering for Schrödinger Operators, J. Fac. Sci. Univ. Tokyo, Sec 1 A, T. 17, 1970, pp. 315-329. Zbl0222.47004MR412635
  7. [7] M.Sh. Birman and D.R. Yafaev, Asymptotics of the Spectrum of a Scattering Matrix, Zap. Nauchn. Sem. Leningrad Otdel Mat. Inst. Steklov (LOMI), T. 110, 1981, pp. 3-29 (Russian). Zbl0501.35064MR643971
  8. [8] T. Kato, Monotonicity Theorems in Scattering Theory, Hadronic J, T. 1, 1978, pp. 134- 154. Zbl0426.47004MR506116
  9. [9] D.R. Yafaev, On the Asymptotics of Scattering Phases for the Schrödinger Equation, Ann. Inst. H. Poincaré, T. 53, 1990, pp.283-299. Zbl0723.35062MR1084881
  10. [10] D.R. Yafaev, Mathematical Scattering Theory: General Theory, Amer. Math. Soc., 1992. Zbl0761.47001
  11. [11] S.T. Kuroda, Scattering Theory for Differential Operators, J. Math. Soc. Japan, T. 25, 1973, pp. 75-104 and 222-234. Zbl0245.47006MR326435
  12. [12] M.Sh. Birman and D.R. Yafaev, A General Scheme in Stationary Scattering Theory, Topics in Math. Phys., Leningrad Univ., T. 12, 1987, pp. 89-117 (Russian). MR923973
  13. [13] M.Sh. Birman, A Local Condition of the Existence of Wave Operators, Izv. Acad. Sci. U.S.S.R., S. Math. T. 32, 1968, pp. 914-942 (Russian). Zbl0169.16903MR248558
  14. [14] L. Hörmander, The Analysis of Linear Partial Differential Operators, II, Springer-Verlag, 1983. Zbl0521.35002MR705278
  15. [15] D.R. Yafaev, The Eikonal Approximation and the Asymptotics of the Total Scattering Cross-Section for the Schrödinger Equation, Ann. Inst. H. Poincaré, T. 44, 1986, pp. 397-425. Zbl0608.35054MR850898
  16. [16] M.Sh. Birman and D.R. Yafaev, On the Trace-Class Method in Potential Scattering Theory, Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov (LOMI), T. 171, 1989, pp. 12-35 (Russian). Zbl0725.47009MR1031982
  17. [17] A.V. Sobolev and D.R. Yafaev, Spectral Properties of the Abstract Scattering Matrix, Trudy MIAN, T. 188, 1990, pp. 125-149 (Russian). Zbl0733.47011MR1100541

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