Book Review
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Book Information:
Authors:
Paulo D. Cordaro and
Francois Trèves
Title:
Hyperfunctions on hypo-analytic manifolds
Additional book information:
Ann. of Mathematics Studies, vol. 136, Princeton Univ. Press,
Princeton, NJ,
1994,
xx + 377 pp.,
ISBN 0-691-92992-X,
$29.95$
1 P. Cordaro and F. Trèves, Necessary and sufficient conditions for the local solvability of hyperfunctions in a class of systems of complex vectors fields, Inventiones Math 120. 339-360 (1995). CMP 1995 11:58G
Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
Masaki Kashiwara and Pierre Schapira, Sheaves on manifolds, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1990. With a chapter in French by Christian Houzel. MR 1074006, DOI 10.1007/978-3-662-02661-8
Hikosaburo Komatsu, Microlocal analysis in Gevrey classes and in complex domains, Microlocal analysis and applications (Montecatini Terme, 1989) Lecture Notes in Math., vol. 1495, Springer, Berlin, 1991, pp. 161–236. MR 1178558, DOI 10.1007/BFb0085124
Gilles Lebeau, Fonctions harmoniques et spectre singulier, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 269–291 (French). MR 584087
A. Martineau, Distributions et valeurs au bord des fonctions holomorphes, Theory of Distributions (Proc. Internat. Summer Inst., Lisbon, 1964), Inst. Gulbenkian Ci., Lisbon, 1964, pp. 193–326 (French). MR 0219754
Séminaire Bourbaki. Vol. 1967/1968: Exposés 331-346, W. A. Benjamin, Inc., New York-Amsterdam, 1969 (French). MR 0255335
Mikio Sato, Theory of hyperfunctions. I, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1959), 139–193. MR 114124
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
Johannes Sjöstrand, Singularités analytiques microlocales, Astérisque, 95, Astérisque, vol. 95, Soc. Math. France, Paris, 1982, pp. 1–166 (French). MR 699623
11 J. Sjöstrand, The FBI transform for CR submanifolds of , Pre-publ. Math. Orsay (1982).
J.-M. Trépreau, Sur la propagation des singularités dans les variétés CR, Bull. Soc. Math. France 118 (1990), no. 4, 403–450 (French, with English summary). MR 1090408
- 1
- P. Cordaro and F. Trèves, Necessary and sufficient conditions for the local solvability of hyperfunctions in a class of systems of complex vectors fields, Inventiones Math 120. 339-360 (1995). CMP 1995 11:58G
- 2
- L. Hörmander, The analysis of linear partial differential operators I, Grundlehren Math. Wiss. 256, Springer-Verlag (1983). MR 85g:35002a
- 3
- M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren Math. Wiss. 292, Springer-Verlag (1990). MR 92a:58132
- 4
- H. Komatsu, Microlocal analysis in Gevrey classes and in complex domains, Lecture Notes in Math. 1495, Springer-Verlag (1991). MR 1178558
- 5
- G. Lebeau, Fonctions harmoniques et spectre singulier, Ann. Ec. Norm. Sup. t 13, 269-291 (1980). MR 81m:58072
- 6
- A. Martineau, Distributions et valeurs au bord des fonctions holomorphes, Proc. Inter. Summer Institute Lisbon, 195-326 (1964). MR 36:2833
- 7
- A. Martineau, Théorèmes de prolongement analytique du type ``Edge of the wedge theorem'', Sém. Bourbaki, 20 ème anné, Exp. 340 (1967-68). MR 41:3
- 8
- M. Sato, Theory of hyperfunctions I, II, J. Fac. Sci. Univ. Tokyo t 8, 139-193, 387-437 (1959 -1960). MR 22:4951; MR 24A:2237
- 9
- M. Sato, T. Kawai, and M. Kashiwara, Hyperfunctions and pseudo-differential equations, Lecture Notes in Mathematics 287, 265-529, Springer-Verlag (1973). MR 54:8747
- 10
- J. Sjöstrand, Singularités analytiques microlocales, Astérisque 95, Soc. Math. France (1982). MR 84m:58151
- 11
- J. Sjöstrand, The FBI transform for CR submanifolds of , Pre-publ. Math. Orsay (1982).
- 12
- J. M. Trépreau, Sur la propagation des singularités dans les variétés CR, Bull. Soc. Math. France 118, 403--450 (1990). MR 92b:58229
Review Information:
Reviewer:
Pierre Schapira
Affiliation:
Université Pierre et Marie Curie (Paris-VI)
Email:
schapira@mathp6.jussieu.fr
Journal:
Bull. Amer. Math. Soc.
33 (1996), 115-118
DOI:
https://doi.org/10.1090/S0273-0979-96-00628-3
Review copyright:
© Copyright 1996
American Mathematical Society