References
Abhyankar, S.S.: Two notes on formal power series. Proc. Amer. Math. Soc.7, 903–905 (1956)
Abhyankar, S.S., Van der Put, M.: Homomorphisms of analytic local rings. Creile's J.42, 26–60 (1970)
Artin, M.: On the solutions of analytic equations. Invent. Math.5, 277–291 (1968)
Artin, M.: Algebraic approximation of structures over complete local rings. I.H.E.S. Publ. Math.36, 23–58 (1969)
Artin, M.: Algebraic spaces. Math. Monographs. No. 3. New Haven, Conn., Yale University Press 1971
Allan, G.R.: Embedding the algebra of formal power series in a Banach algebra. Proc. London Math. Soc.25, 329–340 (1972)
Becker, J., Zame, W.: Homomorphisms into analytic rings. Proc. Amer. Math. Soc. Summer Institute on Several Complex Variables at Williamstown, Massachusetts, Vol. 30, Part 2, pp. 6–10 (1975)
Becker, J.: Exposé on a conjecture of Tougeron. Ann. Inst. Fourier27, 9–27 (1977)
Becker, J., Gurjar, R.: Curves with large tangent space. Trans. Amer. Math. Soc.242, 285–296 (1978)
Bloom, T.: Operateurs differentials sur les espace analytiques complexe. Seminaire Pierre LeLong. Lecture Notes in Mathematics 71. Berlin, Heidelberg, New York: Springer 1968
Bourbaki, N.: Topologie generale. Paris: Hermann 1961
Carpenter, R.L.: Uniqueness of topology for commutative semisimpleF algebras. Proc. Amer. Math. Soc.29, 113–117 (1971)
Eakin, P., Harris, G.: When φ(f) convergent impliesf is convergent. Math. Ann.229, 201–210 (1977)
Gabrielov, A.M.: The formal relations between analytic functions. Funk. Analiz. Appl.5, 64–65 (1971)
Gabrielov, A.M.: Formal relations between analytic functions. Izv. Akad. Nauk. S.S.R.37, 1056–1088 (1973)
Grauert, H., Remmert, R.: Analytische Stellenalgebraen. Berlin, Heidelberg, New York: Springer 1971
Grothendieck, A.: Techniques de construction en geometrie analytique. Seminaire II, Cartan 13 reme annee 1960/1961
Komatsu, H.: Projective and injective limits of weakly compact sequences of locally convex spaces. J. Math. Soc. Japan19, 366–383 (1967)
Milman, P.: Polynomial and analytic homomorphisms of analytic rings. Math. Ann. (to appear)
Nagata, M.: Local rings. New York: Interscience 1962
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Becker, J., Zame, W.R. Applications of functional analysis to the solution of power series equations. Math. Ann. 243, 37–54 (1979). https://doi.org/10.1007/BF01420205
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DOI: https://doi.org/10.1007/BF01420205