Asymptotic equivalence and summability.
Asymptotic equivalence of sequences and summability.
Asymptotic expansions and acceleration of convergence for higher order iteration processes.
Asymptotic Mercerian theorems involving slowly varying functions
Asymptotic properties of convolution products of sequences.
Asymptotic properties of convolution products of sequences.
Asymptotics of a generalized matrix renewal function.
Asymptotische Mercersätze für holder und cesaro-mitel
Asymptotische Mercersätze für Hölder- und Cesàro-Mittel.
Axiomatic theory of divergent series and cohomological equations
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.