Axiomatic theory of divergent series and cohomological equations

Details Axiomatic theory of divergent series and cohomological equations Axiomatic theory of divergent series and cohomological equations

2007-05-11

arxiv.org/abs/0705.1578v2

Mathematics

Functional Analysis

Scientific paper

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.

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