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Book Review

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Book Information:

Author: H. O. Cordes
Title: Elliptic pseudo-differential operators-an abstract theory
Additional book information: Lecture Notes in Math., vol. 756, Springer-Verlag, Berlin and New York, 1979, 331 pp., $18.00.

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

  • 1. R. Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1-42. MR 367730
  • 2. R. Beals and C. Fefferman, Spatially inhomogeneous pseudodifferential operators, Comm. Pure Appl. Math. 27 (1974), 1-24. MR 352747
  • 3. Louis Boutet de Monvel, On the index of Toeplitz operators of several complex variables, Invent. Math. 50 (1978/79), no. 3, 249–272. MR 520928, https://doi.org/10.1007/BF01410080
  • 4. R. Coifman and Y. Meyer, Au delà des opérateurs pseudodifférentiels, Astérisque 57 (1979), 1-184.
  • 5. H. Cordes, On compactness of commutators of multiplications and convolutions, and bounded-ness of pseudodifferential operators, J. Funct. Anal. 18 (1975), 115-131. MR 377599
  • 6. H. Cordes and E. Herman, Gelfand theory of pseudo-differential operators, Amer. J. Math. 90 (1968), 681-717. MR 454743
  • 7. Ronald G. Douglas, 𝐶*-algebra extensions and 𝐾-homology, Annals of Mathematics Studies, vol. 95, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 571362
  • 8. J. Duistermaat, Fourier integral operators, Courant Inst. Lecture Notes, New York, 1974. MR 451313
  • 9. V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc., Providence, R. I., 1977. MR 516965
  • 10. L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1966, pp. 138-183. MR 383152
  • 11. L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), no. 3, 360–444. MR 517939, https://doi.org/10.1002/cpa.3160320304
  • 12. Roger Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. (N.S.) 3 (1980), no. 2, 821–843. MR 578375, https://doi.org/10.1090/S0273-0979-1980-14825-9
  • 13. T. Kato, Boundedness of some pseudo-differential operators, Osaka J. Math. 13 (1976), 1-9. MR 410477
  • 14. Alexander Nagel and E. M. Stein, Lectures on pseudodifferential operators: regularity theorems and applications to nonelliptic problems, Mathematical Notes, vol. 24, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. MR 549321
  • 15. Gert K. Pedersen, 𝐶*-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
  • 16. I. Singer, Some remarks on operator theory and index theory, Proc. Conf. on K-Theory and Operator Algebras (Athens, Georgia), Lecture Notes in Math., no. 575, Springer-Verlag, New York, 1977, pp. 128-138. MR 467848

Review Information:

Reviewer: Michael E. Taylor
Journal: Bull. Amer. Math. Soc. 5 (1981), 73-77
DOI: https://doi.org/10.1090/S0273-0979-1981-14926-0
American Mathematical Society