Tauberian Relations between the Abel-Type and the Borel-Type Methods of Summability.
B.L.R. Shawyer, G.S. Yang (1971)
Manuscripta mathematica
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B.L.R. Shawyer, G.S. Yang (1971)
Manuscripta mathematica
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Given ⨍ ∈ , denote by s(w,z) its integral over the rectangle [0,w]× [0,z] and by σ(u,v) its (C,1,1) mean, that is, the average value of s(w,z) over [0,u] × [0,v], where u,v,w,z>0. Our permanent assumption is that (*) σ(u,v) → A as u,v → ∞, where A is a finite number. First, we consider real-valued functions ⨍ and give one-sided Tauberian conditions which are necessary and sufficient in order that the convergence (**) s(u,v) → A as u,v → ∞ follow from (*). Corollaries allow these...
M.S. Rangachari (1967)
Mathematische Zeitschrift
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