Men'shov example of a zero-series
From Encyclopedia of Mathematics
The first non-trivial example of a trigonometric series that converges to zero in the complement of a perfect set of measure zero; constructed by D.E. Men'shov [1]. A series with this property is called a zero-series. A problem naturally connected with this notion is that of the uniqueness of a trigonometric series of a function (see Uniqueness set).
References
| [1] | D.E. Men'shov, "Sur l'unicité du développement trigonométrique" C.R. Acad. Sci. Paris , 163 (1916) pp. 433–436 |
| [2] | N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian) |
Comments
References
| [a1] | A. Zygmund, "Trigonometric series" , 1–2 , Cambridge Univ. Press (1988) |
How to Cite This Entry:
Men'shov example of a zero-series. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Men%27shov_example_of_a_zero-series&oldid=12958
Men'shov example of a zero-series. M.I. Voitsekhovskii (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Men%27shov_example_of_a_zero-series&oldid=12958
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098