TY - JOUR

T1 - Condenser capacity, exponential blaschke products and universal covering maps

AU - Mashreghi, Javad

AU - Pouliasis, Stamatis

N1 - Publisher Copyright:
© 2015 American Mathematical Society.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2015

Y1 - 2015

N2 - Let B be an exponential Blaschke product, let C be a compact subset of the unit disc 픻 with positive logarithmic capacity and let Kn = B−1(C) ∩ {z ∈ 픻: |z| ≤ 1 − 2−n}. We give a sharp estimate for the rate of growth of the capacity of the condensers (픻,Kn). Also, we examine a similar problem for universal covering maps of multiply connected Greenian domains and we give a precise formula in the case of doubly connected domains.

AB - Let B be an exponential Blaschke product, let C be a compact subset of the unit disc 픻 with positive logarithmic capacity and let Kn = B−1(C) ∩ {z ∈ 픻: |z| ≤ 1 − 2−n}. We give a sharp estimate for the rate of growth of the capacity of the condensers (픻,Kn). Also, we examine a similar problem for universal covering maps of multiply connected Greenian domains and we give a precise formula in the case of doubly connected domains.

KW - Condenser capacity

KW - Exponential Blaschke products

KW - Lindelöf Principle

KW - Universal covering maps

UR - http://www.scopus.com/inward/record.url?scp=85000788560&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2015-12516-6

DO - 10.1090/S0002-9939-2015-12516-6

M3 - Article

AN - SCOPUS:85000788560

VL - 143

SP - 3547

EP - 3559

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -