منابع مشابه
One-sided Tauberian Theorems for Dirichlet Series Methods of Summability
We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...
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R. C. Buck fl] has shown that if a regular matrix sums every subsequence of a sequence x, then x is convergent. I. J. Maddox [4] improved Buck's theorem by showing that if a non-Schur matrix sums every subsequence of a sequence x, then x is convergent. Actually Maddox proved a stronger result: If x is divergent and A sums every subsequence of x, then A is a Schur matrix, i.e., It should be rema...
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The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in...
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In an optimal control framework, we consider the value VT (x) of the problem starting from state x with finite horizon T , as well as the value Wλ(x) of the λ-discounted problem starting from x. We prove that uniform convergence (on the set of states) of the values VT (·) as T tends to infinity is equivalent to uniform convergence of the values Wλ(·) as λ tends to 0, and that the limits are ide...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1973
ISSN: 0022-314X
DOI: 10.1016/0022-314x(73)90057-7