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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

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: H. O. Cordes
Title: The technique of pseudodifferential operators
Additional book information: Cambridge University Press, 1995, xii +382 pp., ISBN 0-521-28443-0, $34.95$

Authors: A. Unterberger and H. Upmeier
Title: Pseudodifferential analysis on symmetric cones
Additional book information: Studies in Advanced Mathematics, CRC Press, Boca Raton, New York, London, and Tokyo, 1996, iii+216 pp., ISBN 0-8493-7873-7, $59.95$

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

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  • A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. MR 100768, DOI 10.2307/2372441
  • H. O. Cordes, Spectral theory of linear differential operators and comparison algebras, London Mathematical Society Lecture Note Series, vol. 76, Cambridge University Press, Cambridge, 1987. MR 890743, DOI 10.1017/CBO9780511662836
  • A. S. Dynin, Singular operators of arbitrary order on a manifold, Dokl. Akad. Nauk SSSR 141 (1961), 21–23 (Russian). MR 0155205
  • Alain Grigis and Johannes Sjöstrand, Microlocal analysis for differential operators, London Mathematical Society Lecture Note Series, vol. 196, Cambridge University Press, Cambridge, 1994. An introduction. MR 1269107, DOI 10.1017/CBO9780511721441
  • Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307
  • Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
  • J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121
  • Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
  • Didier Robert, Autour de l’approximation semi-classique, Progress in Mathematics, vol. 68, Birkhäuser Boston, Inc., Boston, MA, 1987 (French). MR 897108
  • R. T. Seeley, Refinement of the functional calculus of Calderón and Zygmund, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 521–531. MR 0226450
  • M. A. Shubin, Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987. Translated from the Russian by Stig I. Andersson. MR 883081, DOI 10.1007/978-3-642-96854-9
  • A. Unterberger, Quantification de certains espaces hermitiens symétriques, Séminaire Goulaouic-Schwartz, 1979–1980 (French), École Polytech., Palaiseau, 1980, pp. Exp. No. 16, 13 (French). MR 600701
  • Harald Upmeier, Jordan algebras in analysis, operator theory, and quantum mechanics, CBMS Regional Conference Series in Mathematics, vol. 67, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1987. MR 874756, DOI 10.1090/cbms/067
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    Review Information:

    Reviewer: Alexander Dynin
    Affiliation: Ohio State University
    Journal: Bull. Amer. Math. Soc. 33 (1996), 381-384
    Review copyright: © Copyright 1996 American Mathematical Society