An upper bound for the logarithmic capacity of two intervals

Klaus Schiefermayr

doi:10.1080/17476930701644863

An upper bound for the logarithmic capacity of two intervals

Klaus Schiefermayr

Research Center Wels

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

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	65-75
Number of pages	11
Journal	COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Volume	53
Issue number	1
DOIs	https://doi.org/10.1080/17476930701644863
Publication status	Published - Jan 2008

Keywords

31A15
33E05
Chebyshev constant
Jacobi's elliptic functions
Jacobi's theta functions
Logarithmic capacity
Transfinite diameter
Two intervals

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10.1080/17476930701644863

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KW - Jacobi's elliptic functions

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KW - Transfinite diameter

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An upper bound for the logarithmic capacity of two intervals

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Keywords

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