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Corrigenda : "stabilization in H∞R(D)"
Wick, Brett D. (Georgia Institute of Technology. School of Mathematics)

Data: 2011
Resum: In this corrigenda we outline the necessary changes to the paper [3] so that the main result in that paper is made correct. The mistake the author made in the previous version was that the condition that f1 being positive on the zeros of f2 was not strong enough to guarantee the existence of the logarithm in H∞R(D). In particular, the main result now is the following theorem: Suppose that f1, f2 ∈ H∞ R (D), with kf1k∞, kf2k∞ ≤ 1, with inf z∈D (|f1(z)| + |f2(z)|) = δ > 0. Assume for some ǫ > 0, f1 has the same sign on the set {x ∈ (−1, 1) : |f2(x)| < ǫ}. Then there exists g1, g −1 1 , g2 ∈ H∞ R (D) with kg1k∞, kg2k∞, kg −1 k∞ ≤ C(δ, ǫ) and f1(z)g1(z) + f2(z)g2(z) = 1 ∀ z ∈ D.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, Vol. 55, Núm. 1 (2011) , p. 251-260, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_55111_11

10 p, 135.8 KB

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