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Resonances in an abstract analytic scattering theory. (English) Zbl 0462.47010


MSC:

47A40 Scattering theory of linear operators
81U20 \(S\)-matrix theory, etc. in quantum theory
35P25 Scattering theory for PDEs
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References:

[1] J.E. Avron , I.W. Herbst , Spectral and scattering theory of Schrödinger operators related to the Stark effect . Comm. Math. Phys. , t. 52 , 1977 , p. 239 - 259 . Article | MR 468862 | Zbl 0351.47007 · Zbl 0351.47007 · doi:10.1007/BF01609485
[2] D. Babbitt , E. Balslev , Local distortion technique and unitarity of the S-matrix for the 2-body problem . J. Math. Anal. Appl. , t. 54 , 1976 , p. 316 - 347 . MR 413860
[3] J.M. Combes , Spectral deformation techniques and applications to N-body Schrödinger operator . Proc. Int. Congr. Math. , Vancouver , 1974 , p. 369 - 376 . MR 438949 | Zbl 0341.47002 · Zbl 0341.47002
[4] D. Greenstein , On the analytic continuation of functions which map the upper half plane into itself . J. Math. Anal. Appl. , t. 1 , 1960 , p. 355 - 362 . MR 125953 | Zbl 0096.27401 · Zbl 0096.27401 · doi:10.1016/0022-247X(60)90009-3
[5] I.W. Herbst , Dilation analyticity in constant electric fields I. The two body problem . Comm. Math. Phys. , t. 64 , 1978 , p. 279 - 298 . Article | MR 520094 | Zbl 0447.47028 · Zbl 0447.47028 · doi:10.1007/BF01221735
[6] I.W. Herbst , B. Simon , Stark effect revisited . Phys. Rev. Letters , t. 41 , 1978 , p. 67 - 79 . MR 495908
[7] J. Howland , Puiseux series for resonances at an embedded eigenvalue . Pacific J. Math. , t. 55 , 1974 , p. 157 - 176 . Article | MR 417823 | Zbl 0312.47010 · Zbl 0312.47010 · doi:10.2140/pjm.1974.55.157
[8] A. Jensen , Local distortion technique, resonances and poles of the S-matrix . J. Math. Anal. Appl. , t. 59 , 1977 , p. 505 - 513 . MR 441153 | Zbl 0361.47018 · Zbl 0361.47018 · doi:10.1016/0022-247X(77)90077-4
[9] S.T. Kuroda , Scattering theory for differential operators I. Operator theory . J. Math. Soc. Japan , t. 25 , 1973 , p. 75 - 104 . Article | MR 326435 | Zbl 0245.47006 · Zbl 0245.47006 · doi:10.2969/jmsj/02510075
[10] S.T. Kuroda , Scattering theory for differential operators II. Selfadjoint elliptic operators . J. Math. Soc. Japan , t. 25 , 1973 , p. 222 - 234 . Article | MR 326436 | Zbl 0252.47007 · Zbl 0252.47007 · doi:10.2969/jmsj/02520222
[11] J. Nuttall , Analytic continuation of the off-energy shell scattering amplitude . J. Math. Phys. , t. 8 , 1967 , p. 873 - 877 .
[12] N. Shenk , D. Thoe , Eigenfunction expansions and scattering theory for perturbation of - \Delta . Rocky Mountain J. Math. , t. 1 , 1971 , p. 89 - 125 . MR 287189 | Zbl 0254.47017 · Zbl 0254.47017 · doi:10.1216/RMJ-1971-1-1-89
[13] N. Shenk , D. Thoe , Resonant states and poles of the scattering matrix for perturbations of - \Delta . J. Math. Anal. Appl. , t. 37 , 1972 , p. 467 - 491 . MR 308616 | Zbl 0229.35072 · Zbl 0229.35072 · doi:10.1016/0022-247X(72)90289-2
[14] B. Simon , Resonances and complex scaling. A Rigorous overview . Int. J. Quantum Chemistry , t. 14 , 1978 , p. 529 .
[15] L. Thomas , On the spectral properties of some one particle Schrödinger Hamiltonians . Helv. Phys. Acta , t. 45 , 1973 , p. 1057 - 1065 . MR 376023
[16] K. Yajima , Spectral and scattering theory for Schrödinger operators with Stark effect I . J. Fac. Sci. Univ. Tokyo , Sec. IA, t. 26 , 1979 , p. 377 - 390 . MR 560003 | Zbl 0429.35027 · Zbl 0429.35027
[17] K. Yajima , Spectral and scattering theory for Schrödinger operators with Stark effect II . Preprint. MR 617860 · Zbl 0465.35024
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