Authors
Citation
W. Hansen et N. Nadirashvili, LITTLEWOOD ONE CIRCLE PROBLEM, Journal of the London Mathematical Society, 50, 1994, pp. 349-360
Citations number
19
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
00246107
Volume
50
Year of publication
1994
Part
2
Pages
349 - 360
Database
ISI
SICI code
0024-6107(1994)50:<349:LOCP>2.0.ZU;2-W
Abstract
It is shown that Littlewood's one circle problem has a negative answer
, that is, there exists a continous bounded function f on the unit dis
k U such that f is not harmonic, but nevertheless for every x is-an-el
ement-of U the equality f(x) = 1/2pi integral-2pi/0 f(x + r(x)e(it))dt
holds for some r(x) with 0 < r(x) < 1 - parallel-to x parallel-to.