×
Schapira, Pierre

Conditions de positivite dans une variété symplectique complexe. Application à l’étude des microfonctions. (French) Zbl 0473.58022

Ann. Sci. Éc. Norm. Supér. (4) 14, 121-139 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0473.58022

Cited in 3 Reviews
Cited in 14 Documents

MSC:

58J15 Relations of PDEs on manifolds with hyperfunctions
58J32 Boundary value problems on manifolds

Keywords:

pseudo-convex open set with real analytic boundary in a complex analytic manifold; exterior conormal bundle; sheaf of microfunctions; hypoellipticity of microdifferential operators

Citations:

Zbl 0306.42007
Cite Review PDF
Full Text: DOI Numdam EuDML

References:

[1] M. S. BAOUENDI , F. TREVES et E. C. ZACHMANOGLOU , Flat Solutions and Singular Solutions of Homogeneous Linear Partial Differential Equations with Analytic Coefficients (Duke Math. J. vol. 46, n^\circ 2, 1979 , p. 409-440). Article | MR 80h:35034 | Zbl 0418.35003 · Zbl 0418.35003 · doi:10.1215/S0012-7094-79-04618-0
[2] L. BOUTET DE MONVEL , Convergence dans le domaine complexe des séries de fonctions propres (C. R. Acad. Sc., Paris, t. 287, série A, 1978 , p. 855-856). MR 80i:58040 | Zbl 0392.35043 · Zbl 0392.35043
[3] M. KASHIWARA , Exposés à l’Université Paris-Nord, 1976 , non publiés et cours à l’Université Paris-Nord, 1976 - 1977 .
[4] M. KASHIWARA et T. KAWAI , Some Applications of Boundary Value Problems for Elliptic Systems of Linear Differential Equations (Ann. of Math. Studies, n^\circ 93, Princeton, Princeton Univ. Press. 1980 ). MR 81i:35062 | Zbl 0454.46033 · Zbl 0454.46033
[5] M. KASHIWARA et P. SCHAPIRA , Problème de Cauchy pour les systèmes microdifférentiels dans le domaine complexe (Invent. Math., vol. 46, 1978 , p. 17-38). MR 80a:58031 | Zbl 0369.35061 · Zbl 0369.35061 · doi:10.1007/BF01390101
[6] M. KASHIWARA et P. SCHAPIRA , Micro-Hyperbolic Systems (Acta Mathematica, vol. 142, 1979 , p. 1-55). MR 80b:58060 | Zbl 0413.35049 · Zbl 0413.35049 · doi:10.1007/BF02395056
[7] A. MELIN et J. SJÖSTRAND , Fourier Integral Operators with Complex Valued Phase Functions (Lecture Notes in Math., n^\circ 459, Springer, 1975 , p. 120-223). MR 55 #4290 | Zbl 0306.42007 · Zbl 0306.42007
[8] A. MELIN et J. SJÖSTRAND , Fourier Integral Operator with Complex Phase Functions and Parametrix for an Interior Boundary Value Problem (Comm. Partial Diff. Eq., vol. 1, 1976 , p. 313-400). MR 56 #13294 | Zbl 0364.35049 · Zbl 0364.35049 · doi:10.1080/03605307608820014
[9] Ph. PALLU DE LA BARRIÈRE , Existence et prolongement des solutions holomorphes des équations aux dérivées partielles (J. Math. pures et Appl., t. 55, 1976 p. 21-46). MR 54 #3025 | Zbl 0293.35018 · Zbl 0293.35018
[10] J. PERSSON , Local Analytic Continuation of Holomorphic Solutions of Partial Differential Equation (Ann. Mat. pura appl., vol. 4, n^\circ 112, 1977 , p. 193-204). MR 55 #8406 | Zbl 0345.35002 · Zbl 0345.35002 · doi:10.1007/BF02413481
[11] M. SATO , T. KAWAI et M. KASHIWARA , Hyperfunctions and Pseudodifferential Equations (Lecture Notes in Math., n^\circ 287, Springer, 1973 , p. 265-529). MR 54 #8747 | Zbl 0277.46039 · Zbl 0277.46039
[12] P. SCHAPIRA , Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles II (Séminaire Goulaouic-Schwartz, 1976 - 1977 ), exposé n^\circ 9). Numdam | Zbl 0361.35062 · Zbl 0361.35062
[13] P. SCHAPIRA , Rencontre sur les E.D.P. linéaires , Saint-Cast, mai 1979 .
[14] P. SCHAPIRA , C. R. Acad. Sc., Paris, t. 289, série A, 1979 , p. 783-785. MR 80k:32025 | Zbl 0424.32006 · Zbl 0424.32006
[15] J. SJÖSTRAND , Applications of Fourier Distributions with Complex Phase Functions (Lecture Notes in Math., n^\circ 459, Springer, 1975 , p. 255-282). Zbl 0322.35075 · Zbl 0322.35075
[16] J. TSUNO , On the Prolongation of Local Holomorphic Solutions of Partial Differential Equations (J. Math. Soc. Japan, vol. 26, 1974 , p. 523-548). Article | MR 50 #13834 | Zbl 0279.35012 · Zbl 0279.35012 · doi:10.2969/jmsj/02630523
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.