A1 Refereed original research article in a scientific journal
AN EXTREMAL DECOMPOSITION PROBLEM FOR HARMONIC MEASURE
Authors: Dubinin VN, Vuorinen M
Publisher: AMER MATHEMATICAL SOC
Publication year: 2012
Journal: Proceedings of the American Mathematical Society
Journal name in source: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Journal acronym: P AM MATH SOC
Number in series: 7
Volume: 140
Issue: 7
First page : 2441
Last page: 2446
Number of pages: 6
ISSN: 0002-9939
DOI: https://doi.org/10.1090/S0002-9939-2011-11109-2(external)
Abstract
is greater than or equal to the harmonic measure omega(rho, E*, D*), where E* = {z : z(n) is an element of [-1,0]) and D* = {z : vertical bar z vertical bar < 1, vertical bar arg z vertical bar < pi/n}. This implies, for instance, a solution to a problem of R. W. Barnard, L. Cole, and A. Yu. Solynin concerning a lower estimate of the quantity inf (E) max(k=1), ..., (n) omega(a(k), E, D-k) for arbitrary points of the circle vertical bar z vertical bar = p. These authors stated this hypothesis in the particular case when the points are equally distributed on the circle vertical bar z vertical bar = rho.
is greater than or equal to the harmonic measure omega(rho, E*, D*), where E* = {z : z(n) is an element of [-1,0]) and D* = {z : vertical bar z vertical bar < 1, vertical bar arg z vertical bar < pi/n}. This implies, for instance, a solution to a problem of R. W. Barnard, L. Cole, and A. Yu. Solynin concerning a lower estimate of the quantity inf (E) max(k=1), ..., (n) omega(a(k), E, D-k) for arbitrary points of the circle vertical bar z vertical bar = p. These authors stated this hypothesis in the particular case when the points are equally distributed on the circle vertical bar z vertical bar = rho.
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