TY - JOUR
T1 - A DISCRETE HARMONIC FUNCTION BOUNDED ON A LARGE PORTION OF Z2 IS CONSTANT
AU - Buhovsky, Lev
AU - Logunov, Alexander
AU - Malinnikova, Eugenia
AU - Sodin, Mikhail
N1 - Publisher Copyright:
© 2022
PY - 2022/4/15
Y1 - 2022/4/15
N2 - An improvement of the Liouville theorem for discrete harmonic functions on Z2 is obtained. More precisely, we prove that there exists a positive constant " such that if u is discrete harmonic on Z2 and for each sufficiently large square Q centered at the origin \ u\ ≤ 1 on a (1 − ε ) portion of Q, then u is constant.
AB - An improvement of the Liouville theorem for discrete harmonic functions on Z2 is obtained. More precisely, we prove that there exists a positive constant " such that if u is discrete harmonic on Z2 and for each sufficiently large square Q centered at the origin \ u\ ≤ 1 on a (1 − ε ) portion of Q, then u is constant.
UR - http://www.scopus.com/inward/record.url?scp=85130260882&partnerID=8YFLogxK
U2 - 10.1215/00127094-2021-0037
DO - 10.1215/00127094-2021-0037
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85130260882
SN - 0012-7094
VL - 171
SP - 1349
EP - 1378
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 6
ER -