منابع مشابه
On lacunary series with random gaps
We prove Strassen’s law of the iterated logarithm for sums ∑N k=1 f(nkx), where f is a smooth periodic function on the real line and (nk)k≥1 is an increasing random sequence. Our results show that classical results of the theory of lacunary series remain valid for sequences with random gaps, even in the nonharmonic case and if the Hadamard gap condition fails.
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be a power series with the radius of convergence 1. We say that it has Ostrowski gaps p if there exists a pi, such that | an \ < pn for mk á « Û «*. It has infinite Ostrowski gaps p (pp there corresponds a pair of infinite sequences mk and nk (depending on p') with mk<nk and lim nk/mk= « such that | a» | ...
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Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...
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We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1983
ISSN: 0021-9045
DOI: 10.1016/0021-9045(83)90064-3