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Book Review

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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 https://doi.org/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
  • 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
  • Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI https://doi.org/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 https://doi.org/10.1002/cpa.3160180121
  • J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, 1955. MR 16:654a
  • 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
  • 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
  • H. Weyl, The theory of groups and quantum mechanics, Dover, 1950.


Review Information:

Reviewer: Alexander Dynin
Affiliation: Ohio State University
Email: dynin@math.ohio-state.edu
Journal: Bull. Amer. Math. Soc. 33 (1996), 381-384
DOI: https://doi.org/10.1090/S0273-0979-96-00667-2
Review copyright: © Copyright 1996 American Mathematical Society