Inverse scattering theory for Dirac operators

Hiroshi Isozaki

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 66, Issue: 2, page 237-270
  • ISSN: 0246-0211

How to cite

top

Isozaki, Hiroshi. "Inverse scattering theory for Dirac operators." Annales de l'I.H.P. Physique théorique 66.2 (1997): 237-270. <http://eudml.org/doc/76752>.

@article{Isozaki1997,
author = {Isozaki, Hiroshi},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {reconstruction of the potential; scattering matrix},
language = {eng},
number = {2},
pages = {237-270},
publisher = {Gauthier-Villars},
title = {Inverse scattering theory for Dirac operators},
url = {http://eudml.org/doc/76752},
volume = {66},
year = {1997},
}

TY - JOUR
AU - Isozaki, Hiroshi
TI - Inverse scattering theory for Dirac operators
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 66
IS - 2
SP - 237
EP - 270
LA - eng
KW - reconstruction of the potential; scattering matrix
UR - http://eudml.org/doc/76752
ER -

References

top
  1. [1] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. d'Anal. Math., Vol. 30, 1976, pp. 1-38. Zbl0335.35013MR466902
  2. [2] E. Balslev, B. Helffer, Limiting absorption principle and resonances for the Dirac operator, Adv. in Appl. Math., Vol. 13, 1992, pp. 186-215. Zbl0756.35062MR1162140
  3. [3] R. Beals and R. Coifman, Multidimensional inverse scattering and nonlinear P.D.E., Proc. Sympo. Pure Math., Vol. 43, 1985, pp. 45-70. Zbl0575.35011
  4. [4] A. Boutet de Monvel-Berthier, D. Manda and R. Purice, Limiting absorption principle for the Dirac operator, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 58, 1993, pp. 413-431. Zbl0789.35134MR1241704
  5. [5] G. Eskiń and J. Ralston, Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy, Commun. Math. Phys, Vol. 173, 1995, pp. 199-224. Zbl0843.35133MR1355624
  6. [6] L.D. Faddeev, Inverse problem of quantum scattering theory, J. Sov. Math., Vol. 5, 1976, pp. 334-396. Zbl0373.35014
  7. [7] G. Hachem, The ∂-approach to inverse scattering for Dirac operators, Inverse Problems, Vol. 11, 1995, pp. 123-146. Zbl0821.35115MR1313603
  8. [8] V. Isakov, Uniqueness and stability in multi-dimensional inverse problems, Inverse Problems, Vol. 9, 1993, pp. 579-621 Zbl0924.35195MR1251194
  9. [9] H. Isozaki, Multi-dimensional inverse scattering theory for Schrödinger operators, to appear in Reviews in Math. Phys.. Zbl0859.35083MR1405765
  10. [10] S.T. Kuroda, Scattering theory for differential operators, II, J. Math. Soc. Japan, Vol. 25, 1972, pp. 222-234. Zbl0252.47007MR326436
  11. [11] A. Nachman, Reconstruction from boundary measurements, Ann. Math., Vol. 128, 1988, pp. 531-576. Zbl0675.35084MR970610
  12. [12] A. Nachman, Inverse scattering at fixed energy, Proceedings of the 10th International Congress on Math. Phys., Leipzig1991, edited by K. Schmügen, Springer Verlag, 1992, pp. 434-441. Zbl0947.81562MR1386440
  13. [13] A.I. Nachman and M.J. Ablowitz, A multi-dimensional inverse scattering method, Stud. Appl. Math., Vol. 71, 1984, pp. 243-250. Zbl0557.35032
  14. [14] G. Nakamura and G. Uhlman, Global uniqueness for an inverse bounday problem arising in elasticity, Invent. math., Vol. 118, 1994, pp. 457-474. Zbl0814.35147MR1296354
  15. [15] R.G. Newton, Inverse Schrödinger Scattering in Three Dimensions, Springer-Verlag, Berlin-Heidelberg-New York, 1989. Zbl0697.35005MR1029031
  16. [16] R.G. Novikov and G.M. Khenkin, The ∂-equation in the multi-dimensional inverse scattering problem, Russian Math. Surveys, Vol. 42, 1987, pp. 109-180. Zbl0674.35085
  17. [17] R.G. Novikov, The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential, Commun. Math. Phys., Vol. 161, 1994, pp. 569-595. Zbl0803.35166MR1269391
  18. [18] P. Ola, L. Päivärinta and E. Somersalo, An inverse boundary value problem in electrodynamics, Duke Math. J., Vol. 70, 1993, pp. 617-653. Zbl0804.35152MR1224101
  19. [19] J. Sylvester and G. Uhlman, A global uniqueness theorem for an inverse boundary value problem, Ann. Math., Vol. 125, 1987, pp. 153-169. Zbl0625.35078MR873380
  20. [20] B. Thaller, Dirac Equations, Texts and Monographs in Physics, Springer, Berlin1992. MR1219537
  21. [21] B. Thaller, V. Enss, Asympotic observables and Coulomb scattering for the Dirac equation, Ann. Inst. H. Poincaré, Vol. 45, 1986, pp. 147-171. Zbl0615.47008MR866913
  22. [22] G. Uhlmann, Inverse boundary value problems and applications, Astérisque, Vol. 207, 1992, pp. 153-211. Zbl0787.35123MR1205179
  23. [23] R. Weder, Generalized limiting absorption method and multidimensional inverse scattering theory, Math. Meth. in Appl. Sci., Vol. 14, 1991, pp. 509-524. Zbl0738.35055MR1125019
  24. [24] O. Yamada, Eigenfunction expansions and scattering theory for Dirac operators, Publ. RIMS. Kyoto Univ., Vol. 11, 1976, pp. 651-689. Zbl0334.35060MR407471

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.