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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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Full text of review: PDF   This review is available free of charge.
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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  • Hellmut Baumgärtel and Manfred Wollenberg, Mathematical scattering theory, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], vol. 59, Akademie-Verlag, Berlin, 1983. MR 699113, DOI 10.1007/978-3-0348-5440-5
  • M. Sh. Birman and D. R. Yafaev, A general scheme in the stationary theory of scattering, Wave propagation. Scattering theory (Russian), Probl. Mat. Fiz., vol. 12, Leningrad. Univ., Leningrad, 1987, pp. 89–117, 257–258 (Russian). MR 923973
  • M. Sh. Birman and D. R. Yafaev, The spectral shift function. The papers of M. G. Kreĭn and their further development, Algebra i Analiz 4 (1992), no. 5, 1–44 (Russian); English transl., St. Petersburg Math. J. 4 (1993), no. 5, 833–870. MR 1202723
  • Volker Enss, Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials, Comm. Math. Phys. 61 (1978), no. 3, 285–291. MR 523013
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • Tosio Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 99–131. MR 0385603
  • Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys. 78 (1980/81), no. 3, 391–408. MR 603501
  • D. B. Pearson, Quantum scattering and spectral theory, Techniques of Physics, vol. 9, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1988. MR 1099604
  • Leo F. Epstein, A function related to the series for $e^{e^x}$, J. Math. Phys. Mass. Inst. Tech. 18 (1939), 153–173. MR 58, DOI 10.1002/sapm1939181153
    • [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
    DOI: https://doi.org/10.1090/S0273-0979-96-00679-9
    Review copyright: © Copyright 1996 American Mathematical Society