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Book Review

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Book Information:

Author: D. R. Yafaev
Title: Mathematical scattering theory: General theory
Additional book information: Transl. Math. Monographs, vol. 105, Amer. Math. Soc., Providence, RI, 1992, x + 341 pp., ISBN 0-8218-4558-6, $216.00

References [Enhancements On Off] (What's this?)

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  • [BW] H. Baumgärtel and M. Wollenberg, Mathematical Scattering Theory, Akademie-Verlag, Berlin, 1983. MR 86c:47006a
  • [BY] M. Sh. Birman and D. R. Yafaev, A general scheme in stationary scattering theory, Problemy Mat. Fiz., 12(1987), 89--117. MR 89b:47016
  • [BY2] ------, The spectral shift function. The papers of M. G. Krein and their further development, Algebra i Analiz 4(1992), 1--44 (Russian); English translation in St. Petersburg Math. J. 4(1993), 833--870. MR 94g:47002
  • [E] V. Enss, Asymptotic completeness for quantum mechanical potential scattering, I. Short range potentials, Comm. Math. Phys. 61(1978), 285--291. MR 58:25583
  • [K] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, 1966, 1976. MR 34:3324, 53:11389
  • [KK] T. Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, F. E. Browder ed., Functional Analysis and Related Fields, Springer, 1970, 99--131. MR 52:6464a
  • [LP] P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, 1967. MR 36:530
  • [M] E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math, Phys. 91(1979), 91--94. MR 82c:47030
  • [P] D. B. Pearson, Quantum Scattering and Spectral Theory, Academic Press, 1988. MR 91k:81198
  • [RS] M. Reed and B. S. Simon, Methods of Modern Mathematical Physics, Academic Press: vol. I Functional Analysis, 1972; vol. II Fourier Analysis, Self-adjointness, 1975; vol. III Scattering Theory, 1979; vol. IV Analysis of Operators, 1978. MR 58:12429a, 58:12429b, 80m:81085, 58:12429c
  • [SY] A. V. Sobolev and D. R. Yafaev, Spectral properties of the abstract scattering matrix, Trudy Mat. Inst. Steklov 188(1990), 125--149; English translation, Proc. Steklov Inst. Math. 1991, no.3, 159--189.

Review Information:

Reviewer: S. T. Kuroda
Affiliation: Gakushuin University
Email: kuroda@math.gakushuin.ac.jp
Journal: Bull. Amer. Math. Soc. 33 (1996), 467-472
MSC (1991): Primary 47A40, 47A55; Secondary 35P25, 81Uxx
DOI: https://doi.org/10.1090/S0273-0979-96-00679-9
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society