Universal Taylor series with maximal cluster sets
نویسندگان
چکیده
منابع مشابه
Large subspaces of compositionally universal functions with maximal cluster sets
Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (φn), we construct an H(G)-dense linear manifold –as well as a closed infinite-dimensional linear manifold– all of whose non-zero functions have H(G)-dense orbits under the action of the sequence of composition operators associated to (φn). Simultaneously, these functions a...
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We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G. We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its C...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2009
ISSN: 0213-2230
DOI: 10.4171/rmi/582