Bulletin (New Series) of the American Mathematical Society

Review: Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura, Foundations of algebraic analysis

J. L. Brylinsky
Source: Bull. Amer. Math. Soc. (N.S.) Volume 18, Number 1 (1988), 104-108.
First Page: Show Hide

Reviewed Works:

Masaki Kashiwara, Takahiro Kawai, Tatsuo Kimura, Foundations of algebraic analysis. Translated by Goro Kato. Princeton Mathematical Series, vol. 37, Princeton University Press, Princeton, 1986, xii + 254 pp., $38.00. ISBN 0-691-08413-0

Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bams/1183554451

References

1. I. N. Bernstein, Modules over a ring of differential operators, An investigation of the fundamental solutions of equations with constant coefficients, Funktsional. Anal. i Prilozhen. 5 (1971), 89-101.
Zentralblatt MATH: 0233.47031
Mathematical Reviews (MathSciNet): MR290097
2. I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Funktsional. Anal. i Prilozhen 6 (1972), 26-40.
Zentralblatt MATH: 0282.46038
Mathematical Reviews (MathSciNet): MR320735
3. J. E. Björk, Rings of differential operators, North-Holland, 1980.
Zentralblatt MATH: 0499.13009
Mathematical Reviews (MathSciNet): MR549189
4. L. Boutet de Monvel and P. Kree, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier (Grenoble) 17 (1967), 295-323.
Zentralblatt MATH: 0195.14403
Mathematical Reviews (MathSciNet): MR226170
Digital Object Identifier: doi:10.5802/aif.258
5. I. M. Gel'fand and G. E. Shilov, Generalized functions. Vol. 1, Properties and operations, Academic Press, 1964 (reprinted by Harcourt Brace Jovanovich, 1977).
Zentralblatt MATH: 0115.33101
Mathematical Reviews (MathSciNet): MR166596
6. V. Guillemin, M. Kashiwara and T. Kawai, Seminar on microlocal analysis, Ann. of Math. Studies, no. 93, Princeton Univ. Press, 1980.
Zentralblatt MATH: 0409.00007
7. V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc., Providence, R. I., 1977.
Zentralblatt MATH: 0364.53011
Mathematical Reviews (MathSciNet): MR516965
8. M. Kashiwara, On the holonomic systems of differential equations. II, Invent. Math. 49 (1978), 121-135.
Zentralblatt MATH: 0401.32005
Mathematical Reviews (MathSciNet): MR511186
Digital Object Identifier: doi:10.1007/BF01403082
9. M. Kashiwara, Systems of microdifferential equations, Progress in Math., vol. 34, Birkhäuser, 1983.
Zentralblatt MATH: 0521.58057
Mathematical Reviews (MathSciNet): MR725502
10. M. Kashiwara, B-functions and holonomic systems, Invent. Math. 38 (1976), 33-58.
Zentralblatt MATH: 0354.35082
Mathematical Reviews (MathSciNet): MR430304
Digital Object Identifier: doi:10.1007/BF01390168
11. M. Kashiwara and T. Kawai, On the holonomic systems of linear differential equations (systems with regular singularities). III, Publ. R. I. M. S. Kyoto Univ. 17 (1981), 813-979.
Zentralblatt MATH: 0505.58033
Mathematical Reviews (MathSciNet): MR650216
Digital Object Identifier: doi:10.2977/prims/1195184396
12. Le Dung Trang and Z. Mebkhout, Introduction to linear differential equations, Singularities, Part 2, Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R. I., 1983, pp. 31-63.
Zentralblatt MATH: 0521.14006
13. B. Malgrange, L'involutivité des variétés caractéristiques des systèmes différentiels et microdifférentiels, Séminaire Bourbaki (1977/78) Exp. No. 522; Lecture Notes in Math., vol. 710, Springer-Verlag, Berlin and New York, 1979, pp. 277-289.
Zentralblatt MATH: 0423.46033
Mathematical Reviews (MathSciNet): MR554227
14. B. Malgrange, Polynômes de Bernstein-Sato et cohomologie évanescente, Astérisque 101-102 (1983).
Zentralblatt MATH: 0528.32007
Mathematical Reviews (MathSciNet): MR737934
15. A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki 214 (1961-62), mimeographed, I.H.P., Paris.
Zentralblatt MATH: 0122.34902
16. Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984), 63-88.
Zentralblatt MATH: 0566.32021
Mathematical Reviews (MathSciNet): MR734785
17. T. Oda, Introduction to algebraic analysis of complex manifolds, Adv. Study Pure Math., no. 1, North-Holland, 1983.
Zentralblatt MATH: 0512.14008
Mathematical Reviews (MathSciNet): MR715644
18. M. Sato, M. Kashiwara and T. Kawai, Microfunctions and pseudodifferential equations, Lecture Notes in Math., vol. 287, Springer-Verlag, Berlin and New York, 1973, pp. 264-529.
Zentralblatt MATH: 0277.46039
Mathematical Reviews (MathSciNet): MR420735
19. P. Schapira, Microdifferential systems in the complex domain, Grundlehren Math. Wiss., Springer-Verlag, Berlin and New York, 1985.
Zentralblatt MATH: 0554.32022
Mathematical Reviews (MathSciNet): MR774228
20. T. Yano, b-functions and exponents of hypersurface isolated singularities, Singularities, Part 2, Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R. I., 1983, pp. 641-652.
Zentralblatt MATH: 0547.32004
Mathematical Reviews (MathSciNet): MR713287

2013 © American Mathematical Society

Bulletin (New Series) of the American Mathematical Society

Bulletin (New Series) of the American Mathematical Society

Turn MathJax Off
What is MathJax?