Móricz Ferenc honlapja

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Cím:Summability (C, 1) of integrals on $\bbfR_+$.
Szerző:M\'oricz, Ferenc
Forrás:Analysis, M\"unchen 18, No.1, 1-8 (1998).
Nyelv:English
Absztrakt:The author has extended the result of {\it G. H. Hardy} [A theorem concerning summable series, Cambr. Phil. Soc. Proc. 20, 304-307 (1921; JFM 48.1190.01)] for summability $(C,1)$ of a series of complex numbers $\sum^\infty_{n= 0}a_n$ by the convergence of another series $\sum^\infty_{n= 0} b_n$ where $b_n= \sum^\infty_{k=n} a_k/k+1$, $k= 0,1,2,\dots$ to series whose terms are elements of a Banach space and to integrals of locally integral functions over $\bbfR_+= [0,\infty]$. The analogue of the result $s_n/n\to 0$ as $n\to\infty$ is not true for integrals. Also Tauberian conditions for integrals are established from which convergence follows from $(C,1)$ summability of integrals.} \RV{I.L.Sukla (Orissa) 
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