Approximation by polynomials in two diffeomorphisms
نویسندگان
چکیده
منابع مشابه
L Approximation of maps by diffeomorphisms
It is shown that if d ≥ 2, then every map φ : Ω ⊂ R → Rd of class L∞ can be approximated in the Lp-norm by a sequence of orientationpreserving diffeomorphims φn : Ω̄ → φn(Ω̄). These conclusions hold provided that Ω ⊂ Rd is open, bounded, and that 1 ≤ p < +∞. In addition, φn(Ω̄) is contained in the 1/n-neighborhood of the convex hull of φ(Ω). All these conclusions fail for Ω ⊂ R. The main ingredien...
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These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
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1. Let In ;) be a set of distinct positive integers. According to a theorem of Müntz and Szász, the condition En-' .' =-is necessary and sufficient in order that polynomials in the powers x"' and 1 suffice to approximate uniformly an arbitrary continuous function in the interval 0 < x < 1, i .e ., that these powers span the space C of continuous functions in that interval. If the series converg...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1984
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1984-15203-0