Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

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?)

  • [AJS] Werner O. Amrein, Josef M. Jauch, and Kalyan B. Sinha, Scattering theory in quantum mechanics, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1977. Physical principles and mathematical methods; Lecture Notes and Supplements in Physics, No. 16. MR 0495999
  • [BW] 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
    Hellmut Baumgärtel and Manfred Wollenberg, Mathematical scattering theory, Operator Theory: Advances and Applications, vol. 9, Birkhäuser Verlag, Basel, 1983. MR 781534
  • [BY] 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
  • [BY2] 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
  • [E] Volker Enss, Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials, Comm. Math. Phys. 61 (1978), no. 3, 285–291. MR 0523013
  • [K] T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, 1966, 1976. MR 34:3324, 53:11389
  • [KK] 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
    Tosio Kato and S. T. Kuroda, The abstract theory of scattering, Rocky Mountain J. Math. 1 (1971), no. 1, 127–171. MR 0385604,
  • [LP] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • [M] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys. 78 (1980/81), no. 3, 391–408. MR 603501
  • [P] D. B. Pearson, Quantum scattering and spectral theory, Techniques of Physics, vol. 9, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1988. MR 1099604
  • [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
Journal: Bull. Amer. Math. Soc. 33 (1996), 467-472
Review copyright: © Copyright 1996 American Mathematical Society