Inverse scattering theory for Dirac operators
Annales de l'I.H.P. Physique théorique (1997)
- Volume: 66, Issue: 2, page 237-270
- ISSN: 0246-0211
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topIsozaki, 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] 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] 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] 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] 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] 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] L.D. Faddeev, Inverse problem of quantum scattering theory, J. Sov. Math., Vol. 5, 1976, pp. 334-396. Zbl0373.35014
- [7] G. Hachem, The ∂-approach to inverse scattering for Dirac operators, Inverse Problems, Vol. 11, 1995, pp. 123-146. Zbl0821.35115MR1313603
- [8] V. Isakov, Uniqueness and stability in multi-dimensional inverse problems, Inverse Problems, Vol. 9, 1993, pp. 579-621 Zbl0924.35195MR1251194
- [9] H. Isozaki, Multi-dimensional inverse scattering theory for Schrödinger operators, to appear in Reviews in Math. Phys.. Zbl0859.35083MR1405765
- [10] S.T. Kuroda, Scattering theory for differential operators, II, J. Math. Soc. Japan, Vol. 25, 1972, pp. 222-234. Zbl0252.47007MR326436
- [11] A. Nachman, Reconstruction from boundary measurements, Ann. Math., Vol. 128, 1988, pp. 531-576. Zbl0675.35084MR970610
- [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] 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] 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] R.G. Newton, Inverse Schrödinger Scattering in Three Dimensions, Springer-Verlag, Berlin-Heidelberg-New York, 1989. Zbl0697.35005MR1029031
- [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] 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] 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] 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] B. Thaller, Dirac Equations, Texts and Monographs in Physics, Springer, Berlin1992. MR1219537
- [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] G. Uhlmann, Inverse boundary value problems and applications, Astérisque, Vol. 207, 1992, pp. 153-211. Zbl0787.35123MR1205179
- [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] O. Yamada, Eigenfunction expansions and scattering theory for Dirac operators, Publ. RIMS. Kyoto Univ., Vol. 11, 1976, pp. 651-689. Zbl0334.35060MR407471
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