منابع مشابه
Illumination by Taylor Polynomials
Let f(x) be a differentiable function on the real line R, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass through P . We prove that if f ′′ is continuous and nonnegative on R, f ′′ ≥ m > 0 outside a closed interval of R, and f ′′ has finitely many zeros onR, then any point P below the graph of f...
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We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...
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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: Journal of Mathematical Analysis and Applications
سال: 1990
ISSN: 0022-247X
DOI: 10.1016/0022-247x(90)90296-r