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References
Artin, M., On the solutions of analytic equations,Invent. Math.,5 (1968), 277–291.
Bochnak, J., Siciak, J., Analytic functions in topological vector spaces,Studia Math.,39 (1971), 77–112.
Bourbaki, N.,Variétés différentielles et analytiques, Hermann, 1967.
Colombeau, J.-F.,Différentiation et bornologie, Thèse, Université de Bordeaux, 1973.
Galligo, A., Théorème de division et stabilité en géométrie analytique locale,Ann. Inst. Fourier,29, 2 (1979), 107–184.
Grothendieck, A.,Topological vector spaces, Gordon and Breach, 1973.
Grauert, H., Remmert, R.,Analytische Stellenalgebren, Springer, 1971.
Hamilton, R. S., The inverse function theorem of Nash and Moser,Bull. Amer. Math. Soc.,7 (1982), 65–222.
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.
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.
Hauser, H., Müller, G., Affine varieties and Lie algebras of vector fields,Manuscr. Math.,80 (1993), 309–337.
Hervé, M., Analyticity in infinite dimensional spaces,Studies in Math.,10, De Gruyter, 1989.
Leslie, J., On the group of real analytic diffeomorphisms of a compact real analytic manifold,Trans. Amer. Math. Soc.,274 (1982), 651–669.
Milnor, J., Remarks on infinite-dimensional Lie groups, inRelativité, groupes et topologie II, Les Houches, Session XL, 1983 (eds :de Witt etStora), p. 1007–1057, Elsevier, 1984.
Müller, G., Reduktive Automorphismengruppen analytischer C-Algebren,J. Reine Angew. Math.,364 (1986), 26–34.
Müller, G., Deformations of reductive group actions,Proc. Camb. Philos. Soc.,106 (1989), 77–88.
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.
Pisanelli, D., The proof of Frobenius Theorem in a Banach scale, inFunctional analysis, holomorphy and approximation theory (ed.G. I. Zapata), p. 379–389, Marcel Dekker, 1983.
Pisanelli, D., The proof of the Inversion Mapping Theorem in a Banach scale, inComplex analysis, functional analysis and approximation theory (ed.J. Mujica), p. 281–285, North-Holland, 1986.
Upmeier, H.,Symmetric Banach manifolds and Jordan C*-algebras, North-Holland, 1985.
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Hauser, H., Müller, G. A rank theorem for analytic maps between power series spaces. Publications Mathématiques de L’Institut des Hautes Scientifiques 80, 95–115 (1994). https://doi.org/10.1007/BF02698897
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DOI: https://doi.org/10.1007/BF02698897