Necessary and sufficient conditions under which convergence follows from summability by weighted means.
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function s is slowly...
Negative Resultate über Tauber-Bedingungen.
Noninclusion theorems for summability matrices.
Noninclusion theorems: Some remarks on a paper by J. A. Fridy.
Norm-preserving L-L integral transformations.
Normvergleich bei abschnittsbeschränkten Limitierungsverfahren.