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Book Review
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Book Information
Author(s):
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:
- 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.
- L. Boutet de Monvel, On the index of Toeplitz operators of several complex variables, Invent. Math. 50 (1979), 249-272. MR 520928
- 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.
- R. Douglas, C*-algebra extensions and K-homology, Ann. of Math. Studies, No. 95, Princeton Univ. Press, Princeton, N. J., 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), 359-443. MR 517939
- 12.
- R. Howe, On the role of the Heisenberg group in harmonic analysis, Bull. Amer. Math. Soc. (N.S.) 3 (1980), 821-843. MR 578375
- 13.
- T. Kato, Boundedness of some pseudo-differential operators, Osaka J. Math. 13 (1976), 1-9. MR 410477
- 14.
- A. Nagel and E. Stein, Lectures on pseudo-differential operators: Regularity theorems and applications to non-elliptic problems, Math. Notes, Princeton Univ. Press, Princeton, N. J., 1979. MR 549321
- 15.
- G. Pedersen, C*-algebras and their automorphism groups, Academic Press, London, 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
Additional Information:
Reviewer(s):
Michael E.
Taylor
Review Information:
Journal:
Bull. Amer. Math. Soc.
5
(1981),
73-77.
DOI:
10.1090/S0273-0979-1981-14926-0
PII:
S 0273-0979(1981)14926-0
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