Summary
Let K be a complete ultrametric algebraically closed field. Let D be a bounded closed strongly infraconnected set in K with no T-filter, and let H(D) be the Banach algebra of the analytic elements in D. Let r′, r″ be functions from D toR with bounds a, b such that 0<a⩽ ⩽r′(x)<r″(x)⩽b. Let\(\mathfrak{L}\)(D,r′,r″) be the Banach algebra of the Laurent series with coefficients as in H(D) such that\(\mathop {\lim }\limits_{\left| s \right| \to + \infty } ( \mathop {\sup }\limits_{x \in D} \left| {a_s (x)} \right| \max (r'(x)^s ,r''(x)^s )) = 0\), provided with a suitable norm. In\(\mathfrak{L}\)(D, r′, r″) we give a kind of Hensel Factorization for series whose dominating coefficients at r′(x) and at r″(x) conserve the same rank. We take advantage of this method to correcting a mistake that happened in our previous article on the Hensel Factorization for Taylor series.
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And Erratum to «Maximum principle for analytic elements and Lubin-Hensel's Theorem inH(D)〚Y〛»,135, pp. 265–278 of this Journal.
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Escassut, A. Lubin-Hensel factorization for Laurent series. Annali di Matematica pura ed applicata 147, 73–92 (1987). https://doi.org/10.1007/BF01762411
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DOI: https://doi.org/10.1007/BF01762411