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

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

3 Zitate (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.

Originalsprache	Englisch
Seiten (von - bis)	65-75
Seitenumfang	11
Fachzeitschrift	COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Jahrgang	53
Ausgabenummer	1
DOIs	https://doi.org/10.1080/17476930701644863
Publikationsstatus	Veröffentlicht - Jän. 2008

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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.",

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An upper bound for the logarithmic capacity of two intervals

Abstract

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