Condenser capacity, exponential blaschke products and universal covering maps

Javad Mashreghi; Stamatis Pouliasis

doi:10.1090/S0002-9939-2015-12516-6

Condenser capacity, exponential blaschke products and universal covering maps

Javad Mashreghi, Stamatis Pouliasis

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let B be an exponential Blaschke product, let C be a compact subset of the unit disc 픻 with positive logarithmic capacity and let K_n = 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,K_n). 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.

Original language	English
Pages (from-to)	3547-3559
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-2015-12516-6
State	Published - 2015

Keywords

Condenser capacity
Exponential Blaschke products
Lindelöf Principle
Universal covering maps

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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.

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KW - Exponential Blaschke products

KW - Lindelöf Principle

KW - Universal covering maps

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JO - Proceedings of the American Mathematical Society

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