An upper bound for the logarithmic capacity of two intervals

The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals [−1, α]  ∪ [β, 1] has been given explicitly with the help of Jacobi's elliptic and theta functions already by Achieser in 1930. By proving several inequalities for these elliptic and theta fu...

Full description

Saved in:
Bibliographic Details
Published in:Complex variables and elliptic equations 2008-01, Vol.53 (1), p.65-75
Main Author: Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Chebyshev constant
Jacobi's elliptic functions
Jacobi's theta functions
Logarithmic capacity
Transfinite diameter
Two intervals
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The logarithmic capacity (also called Chebyshev constant or transfinite diameter) of two real intervals [−1, α]  ∪ [β, 1] has been given explicitly with the help of Jacobi's elliptic and theta functions already by Achieser in 1930. By proving several inequalities for these elliptic and theta functions, an upper bound for the logarithmic capacity in terms of elementary functions of  α and  β is derived.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476930701644863