ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01762411
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