Axiomatic theory of divergent series and cohomological equations

Yu. I. Lyubich. "Axiomatic theory of divergent series and cohomological equations." Fundamenta Mathematicae 198.3 (2008): 263-282. <http://eudml.org/doc/282647>.

@article{Yu2008,
abstract = {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.},
author = {Yu. I. Lyubich},
journal = {Fundamenta Mathematicae},
keywords = {cohomological equation; divergent series; nonmeasurable function; orbital series; quasiexponential series; summation method},
language = {eng},
number = {3},
pages = {263-282},
title = {Axiomatic theory of divergent series and cohomological equations},
url = {http://eudml.org/doc/282647},
volume = {198},
year = {2008},
}

TY - JOUR
AU - Yu. I. Lyubich
TI - Axiomatic theory of divergent series and cohomological equations
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 3
SP - 263
EP - 282
AB - 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.
LA - eng
KW - cohomological equation; divergent series; nonmeasurable function; orbital series; quasiexponential series; summation method
UR - http://eudml.org/doc/282647
ER -