Bulletin of the American Mathematical Society

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Book Information:

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

I. N. Bernšteĭn, Modules over a ring of differential operators. An investigation of the fundamental solutions of equations with constant coefficients, Funkcional. Anal. i Priložen. 5 (1971), no. 2, 1–16 (Russian). MR 0290097

I. N. Bernšteĭn, Analytic continuation of generalized functions with respect to a parameter, Funkcional. Anal. i Priložen. 6 (1972), no. 4, 26–40. MR 0320735

J.-E. Björk, Rings of differential operators, North-Holland Mathematical Library, vol. 21, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 549189

Louis Boutet de Monvel and Paul Krée, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 1, 295–323 (English, with French summary). MR 226170

I. M. Gel’fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Academic Press, New York-London, 1964. Translated by Eugene Saletan. MR 0166596

6.

V. Guillemin, M. Kashiwara and T. Kawai, Seminar on microlocal analysis, Ann. of Math. Studies, no. 93, Princeton Univ. Press, 1980.

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

Masaki Kashiwara, On the holonomic systems of linear differential equations. II, Invent. Math. 49 (1978), no. 2, 121–135. MR 511186, DOI 10.1007/BF01403082

Masaki Kashiwara, Systems of microdifferential equations, Progress in Mathematics, vol. 34, Birkhäuser Boston, Inc., Boston, MA, 1983. Based on lecture notes by Teresa Monteiro Fernandes translated from the French; With an introduction by Jean-Luc Brylinski. MR 725502

Masaki Kashiwara, $B$-functions and holonomic systems. Rationality of roots of $B$-functions, Invent. Math. 38 (1976/77), no. 1, 33–53. MR 430304, DOI 10.1007/BF01390168

Masaki Kashiwara and Takahiro Kawai, On holonomic systems of microdifferential equations. III. Systems with regular singularities, Publ. Res. Inst. Math. Sci. 17 (1981), no. 3, 813–979. MR 650216, 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.

Bernard Malgrange, L’involutivité des caractéristiques des systèmes différentiels et microdifférentiels, Séminaire Bourbaki, 30e année (1977/78), Lecture Notes in Math., vol. 710, Springer, Berlin, 1979, pp. Exp. No. 522, pp. 277–289 (French). MR 554227

B. Malgrange, Polynômes de Bernstein-Sato et cohomologie évanescente, Analysis and topology on singular spaces, II, III (Luminy, 1981) Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 243–267 (French). MR 737934

15.

A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki 214 (1961-62), mimeographed, I.H.P., Paris.

Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984), no. 1, 63–88 (French). MR 734785

Tadao Oda, Introduction to algebraic analysis on complex manifolds, Algebraic varieties and analytic varieties (Tokyo, 1981) Adv. Stud. Pure Math., vol. 1, North-Holland, Amsterdam, 1983, pp. 29–48. MR 715644, DOI 10.2969/aspm/00110029

Mikio Sato, Takahiro Kawai, and Masaki Kashiwara, Microfunctions and pseudo-differential equations, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, pp. 265–529. MR 0420735

Pierre Schapira, Microdifferential systems in the complex domain, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 269, Springer-Verlag, Berlin, 1985. MR 774228, DOI 10.1007/978-3-642-61665-5

Tamaki Yano, $b$-functions and exponents of hypersurface isolated singularities, Singularities, Part 2 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 641–652. MR 713287, DOI 10.24033/bsmf.1455

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. MR 0290097

2.

I. N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Funktsional. Anal. i Prilozhen 6 (1972), 26-40. MR 320735

3.

J. E. Björk, Rings of differential operators, North-Holland, 1980. MR 549189

4.

L. Boutet de Monvel and P. Kree, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier (Grenoble) 17 (1967), 295-323. MR 226170

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). MR 166596

6.

V. Guillemin, M. Kashiwara and T. Kawai, Seminar on microlocal analysis, Ann. of Math. Studies, no. 93, Princeton Univ. Press, 1980.

7.

V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc., Providence, R. I., 1977. MR 516965

8.

M. Kashiwara, On the holonomic systems of differential equations. II, Invent. Math. 49 (1978), 121-135. MR 511186

9.

M. Kashiwara, Systems of microdifferential equations, Progress in Math., vol. 34, Birkhäuser, 1983. MR 725502

10.

M. Kashiwara, B-functions and holonomic systems, Invent. Math. 38 (1976), 33-58. MR 430304

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. MR 650216

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.

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. MR 554227

14.

B. Malgrange, Polynômes de Bernstein-Sato et cohomologie évanescente, Astérisque 101-102 (1983). MR 737934

15.

A. Martineau, Les hyperfonctions de M. Sato, Séminaire Bourbaki 214 (1961-62), mimeographed, I.H.P., Paris.

16.

Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984), 63-88. MR 734785

17.

T. Oda, Introduction to algebraic analysis of complex manifolds, Adv. Study Pure Math., no. 1, North-Holland, 1983. MR 715644

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. MR 420735

19.

P. Schapira, Microdifferential systems in the complex domain, Grundlehren Math. Wiss., Springer-Verlag, Berlin and New York, 1985. MR 774228

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. MR 713287