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.
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 -