Bulletin of the American Mathematical Society

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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.

Richard Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1–42. MR 367730

Richard Beals and Charles Fefferman, Spatially inhomogeneous pseudodifferential operators. I, Comm. Pure Appl. Math. 27 (1974), 1–24. MR 352747, DOI 10.1002/cpa.3160270102

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, DOI 10.1007/BF01410080

4.

R. Coifman and Y. Meyer, Au delà des opérateurs pseudodifférentiels, Astérisque 57 (1979), 1-184.

H. O. Cordes, On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators, J. Functional Analysis 18 (1975), 115–131. MR 377599, DOI 10.1016/0022-1236(75)90020-8

H. O. Cordes and E. A. Herman, Gel′fand theory of pseudo differential operators, Amer. J. Math. 90 (1968), 681–717. MR 454743, DOI 10.2307/2373478

Ronald G. Douglas, $C^{\ast }$-algebra extensions and $K$-homology, Annals of Mathematics Studies, No. 95, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 571362

J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences, New York University, New York, 1973. Translated from Dutch notes of a course given at Nijmegen University, February 1970 to December 1971. MR 0451313

Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965

Lars Hörmander, Pseudo-differential operators and hypoelliptic equations, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 138–183. MR 0383152

L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), no. 3, 360–444. MR 517939, DOI 10.1002/cpa.3160320304

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, DOI 10.1090/S0273-0979-1980-14825-9

Tosio Kato, Boundedness of some pseudo-differential operators, Osaka Math. J. 13 (1976), no. 1, 1–9. MR 410477

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

Gert K. Pedersen, $C^{\ast }$-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006

I. M. Singer, Some remarks on operator theory and index theory, $K$-theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975) Lecture Notes in Math., Vol. 575, Springer, Berlin, 1977, pp. 128–138. MR 0467848

1.

R. Beals, A general calculus of pseudodifferential operators, Duke Math. J. 42 (1975), 1-42. MR 0367730

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