A rank theorem for analytic maps between power series spaces

Herwig Hauser; Gerd Müller

Publications Mathématiques de l'IHÉS (1994)

  • Volume: 80, page 95-115
  • ISSN: 0073-8301

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Hauser, Herwig, and Müller, Gerd. "A rank theorem for analytic maps between power series spaces." Publications Mathématiques de l'IHÉS 80 (1994): 95-115. <http://eudml.org/doc/104102>.

@article{Hauser1994,
author = {Hauser, Herwig, Müller, Gerd},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {rank theorem; analytic mappings},
language = {eng},
pages = {95-115},
publisher = {Institut des Hautes Études Scientifiques},
title = {A rank theorem for analytic maps between power series spaces},
url = {http://eudml.org/doc/104102},
volume = {80},
year = {1994},
}

TY - JOUR
AU - Hauser, Herwig
AU - Müller, Gerd
TI - A rank theorem for analytic maps between power series spaces
JO - Publications Mathématiques de l'IHÉS
PY - 1994
PB - Institut des Hautes Études Scientifiques
VL - 80
SP - 95
EP - 115
LA - eng
KW - rank theorem; analytic mappings
UR - http://eudml.org/doc/104102
ER -

References

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  2. [BS] BOCHNAK, J., SICIAK, J., Analytic functions in topological vector spaces, Studia Math., 39 (1971), 77-112. Zbl0214.37703MR47 #2365
  3. [B] BOURBAKI, N., Variétés différentielles et analytiques, Hermann, 1967. Zbl0171.22004
  4. [C] COLOMBEAU, J.-F., Différentiation et bornologie, Thèse, Université de Bordeaux, 1973. MR56 #9259
  5. [Ga] GALLIGO, A., Théorème de division et stabilité en géométrie analytique locale, Ann. Inst. Fourier, 29, 2 (1979), 107-184. Zbl0412.32011MR81e:32009
  6. [Gr] GROTHENDIECK, A., Topological vector spaces, Gordon and Breach, 1973. Zbl0275.46001MR51 #8772
  7. [GR] GRAUERT, H., REMMERT, R., Analytische Stellenalgebren, Springer, 1971. Zbl0231.32001MR47 #5290
  8. [Ham] HAMILTON, R. S., The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc., 7 (1982), 65-222. Zbl0499.58003MR83j:58014
  9. [Hau] HAUSER, H., La construction de la déformation semi-universelle d'un germe de variété analytique complexe, Ann. Sci. Ec. Norm. Sup. Paris (4), 18 (1985), 1-56. Zbl0583.32052MR87f:32029
  10. [HM1] HAUSER, H., MÜLLER, G., Automorphism groups in local analytic geometry, infinite dimensional Rank Theorem and Lie groups, C. R. Acad. Sci. Paris, 313 (1991), 751-756. Zbl0744.32017
  11. [HM2] HAUSER, H., MÜLLER, G., Affine varieties and Lie algebras of vector fields, Manuscr. Math., 80 (1993), 309-337. Zbl0805.14004MR94j:17025
  12. [He] HERVÉ, M., Analyticity in infinite dimensional spaces, Studies in Math., 10, De Gruyter, 1989. Zbl0666.58008MR90f:46074
  13. [L] LESLIE, J., On the group of real analytic diffeomorphisms of a compact real analytic manifold, Trans. Amer. Math. Soc., 274 (1982), 651-669. Zbl0513.58017MR85e:58012
  14. [Mi] MILNOR, J., Remarks on infinite-dimensional Lie groups, in Relativité, groupes et topologie II, Les Houches, Session XL, 1983 (eds : DE WITT et STORA), p. 1007-1057, Elsevier, 1984. Zbl0594.22009
  15. [Mü1] MÜLLER, G., Reduktive Automorphismengruppen analytischer C-Algebren, J. Reine Angew. Math., 364 (1986), 26-34. Zbl0569.32003MR88d:32041
  16. [Mü2] MÜLLER, G., Deformations of reductive group actions, Proc. Camb. Philos. Soc., 106 (1989), 77-88. Zbl0683.32021MR90c:32043
  17. [P1] PISANELLI, D., An extension of the exponential of a matrix and a counter example to the inversion theorem of a holomorphic mapping in a space H(K), Rend. Mat. Appl. (6), 9 (1976), 465-475. Zbl0346.32034MR58 #7754
  18. [P2] PISANELLI, D., The proof of Frobenius Theorem in a Banach scale, in Functional analysis, holomorphy and approximation theory (ed. G. I. ZAPATA), p. 379-389, Marcel Dekker, 1983. Zbl0505.34049MR84g:58099
  19. [P3] PISANELLI, D., The proof of the Inversion Mapping Theorem in a Banach scale, in Complex analysis, functional analysis and approximation theory (ed. J. MUJICA), p. 281-285, North-Holland, 1986. Zbl0673.46020MR88i:58012
  20. [U] UPMEIER, H., Symmetric Banach manifolds and Jordan C*-algebras, North-Holland, 1985. Zbl0561.46032MR87a:58022

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