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Littlewood's One Circle Problem
Author(s) -
Hansen W.,
Nadirashvili N.
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.2.349
Subject(s) - bounded function , unit disk , unit circle , mathematics , combinatorics , function (biology) , continuous function (set theory) , harmonic function , unit (ring theory) , physics , pure mathematics , mathematical analysis , mathematics education , evolutionary biology , biology
It is shown that Littlewood's one circle problem has a negative answer, that is, there exists a continuous bounded function f on the unit disk U such that f is not harmonic, but nevertheless for every x ∈ U the equalityf ( x ) = 1 2 π∫ 0 2 πf ( x + r ( x ) e u ) d tholds for some r ( x ) with 0 < r ( x ) < 1 − ∥ x ∥.