Efficient bounds for the spectral shift function
Annales de l'I.H.P. Physique théorique, Tome 58 (1993) no. 1, pp. 55-83.
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     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},
     mrnumber = {1208792},
     zbl = {0813.47006},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1993__58_1_55_0/}
}
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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

[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 | Zbl

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

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

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

[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 | Zbl

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

[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 | Zbl

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

[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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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