Efficient bounds for the spectral shift function
Annales de l'I.H.P. Physique théorique, Tome 58 (1993) no. 1, pp. 55-83.
@article{AIHPA_1993__58_1_55_0,
     author = {Sobolev, A. V.},
     title = {Efficient bounds for the spectral shift function},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {55--83},
     publisher = {Gauthier-Villars},
     volume = {58},
     number = {1},
     year = {1993},
     zbl = {0813.47006},
     mrnumber = {1208792},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1993__58_1_55_0/}
}
TY  - JOUR
AU  - Sobolev, A. V.
TI  - Efficient bounds for the spectral shift function
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1993
DA  - 1993///
SP  - 55
EP  - 83
VL  - 58
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1993__58_1_55_0/
UR  - https://zbmath.org/?q=an%3A0813.47006
UR  - https://www.ams.org/mathscinet-getitem?mr=1208792
LA  - en
ID  - AIHPA_1993__58_1_55_0
ER  - 
Sobolev, A. V. Efficient bounds for the spectral shift function. Annales de l'I.H.P. Physique théorique, Tome 58 (1993) no. 1, pp. 55-83. http://www.numdam.org/item/AIHPA_1993__58_1_55_0/

[1] M.G. Krein, Perturbation Determinants and a Formula for the Traces of Unitary and Self-Adjoint Operators, Soviet Math. Doklady, Vol. 3, 1962, p. 707-710. | Zbl 0191.15201

[2] M. Sh. BIRMAN and M.G. Krein, On the Theory of Wave Operators and Scattering Operators, Soviet Math. Doklady, Vol. 3, 1962, pp. 740-744. | MR 139007 | Zbl 0196.45004

[3] M.G. Krein, Topics in Differential and Integral Equations and Operator Theory, Operator Theory: Advances and Applications, Vol. 7, 1983. | MR 815109 | Zbl 0512.45001

[4] D.R. Yafaev, Mathematical Scattering Theory, I, General Theory, Amer. Math. Soc. (in print). | MR 1180965 | Zbl 0761.47001

[5] E. Mourre, Absence of Singular Spectrum for Certain Self-Adjoint Operators, Comm. Math. Phys., Vol. 78, 1981, pp. 391-408. | MR 603501 | Zbl 0489.47010

[6] I.Z. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, A.M.S., Transl. Math. Monographs, Vol. 18, 1969. | MR 246142 | Zbl 0181.13504

[7] M. Sh. BIRMAN and M.Z. Solomyak, Spectral Theory of Selfadjoint Operators in Hilbert Space, Dordrecht, D. Reidel, P.C., 1987. | MR 1192782 | Zbl 0744.47017

[8] M. Sh. BIRMAN and M.Z. Solomyak, Estimates of Singular Numbers of Integral Operators, Russian Math. Surveys, Vol. 32:1, 1977, pp. 15-89. | MR 438186 | Zbl 0376.47023

[9] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966. | Zbl 0148.12601

[10] M. Sh. BIRMAN and S. Entina, Time Independent Approach in the Abstract Scattering Theory, Izv. Acad. Nauk S.S.S.R., T 31, No. 2, 1967, pp. 401-430 (Russian). | MR 209895

[11] S.N. Naboko, Non-Tangent Boundary Values of Operator R-functions in the Half-Plane, Algebra i Analiz, Vol. 157, 1989, pp. 197-222; Engl. transl.: Leningrad Math. J., Vol. 1, No. 5, 1990. | MR 1036844 | Zbl 0716.47009

[12] M. Klaus, Some Applications of the Birman-Schwinger Principle, Helv. Phys. Acta, Vol. 55, 1982, pp. 49-68. | MR 674865

[13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, London, 1979. | MR 529429 | Zbl 0405.47007

[14] V.S. Bouslaev, Trace Formulae and Some Asymptotic Estimates of the Resolvent Kernel for the Three-Dimensional Schrödinger Operator, Topics in Math. Phys., Vol. 1, 1966, pp. 82-101.

[15] Y. Colin De Verdière, Une formule de trace pour l'opérateur de Schrôdinger dans R3, Ann. Scient. Ec. Norm. Sup., Serie 4, t. 14, 1981, pp. 27-39. | Numdam | MR 618729 | Zbl 0482.35068

[16] L. Guillopé, Asymptotique de la phase de diffusion pour l'opérateur de Schrôdinger dans Rn, Seminaire E.D.P., École Polytechnique, exposé No. 5, 1984-1985. | Numdam | MR 819771 | Zbl 0597.35091

[17] D. Robert, Asymptotique de la phase de diffusion à haute énergie pour les perturbations du laplacien, Séminaire E.D.P., École Polytechnique, exposé No. 17, 1988-1989. | Numdam | MR 1032293 | Zbl 0706.35107

[18] D. Robert and H. Tamura, Semi-Classical Bounds for Resolvents of Schrödinger Operators and Asymptotics for Scattering Phases, Comm. in Part. Diff. Eq., Vol. 9, (10), 1984, pp. 1017-1058. | MR 755930 | Zbl 0561.35021

[19] M. Cwickel, Weak Type Estimates for Singular Values and the Number of Bound States of Schrôdinger Operators, Ann. Math., Vol. 106, 1977, pp. 93-100. | MR 473576 | Zbl 0362.47006

[20] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, London, 1978. | MR 493421 | Zbl 0401.47001