Minimal kernels, quadrature identities and proportional harmonic measures

John R. Akeroyd; Kristi Karber; Alexander Yu Solynin

doi:10.1216/rmjm/1181069346

Minimal kernels, quadrature identities and proportional harmonic measures

John R. Akeroyd, Kristi Karber, Alexander Yu Solynin

Mathematics and Statistics

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

2 Scopus citations

Abstract

We describe nonnegative weights on double struck T sign that are minimal at a given point and are related to quadrature identities for harmonic functions. The problem has a geometric interpretation in terms of a system of crescent regions carrying proportional harmonic measures. This system occurs as circle domains of a quadratic differential with second order poles. Our results have applications to harmonic polynomial approximation.

Original language	English
Pages (from-to)	1819-1844
Number of pages	26
Journal	Rocky Mountain Journal of Mathematics
Volume	36
Issue number	6
DOIs	https://doi.org/10.1216/rmjm/1181069346
State	Published - 2006

Keywords

Harmonic function
Harmonic measure
Polynomial approximation
Quadratic differential
Quadrature identity

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10.1216/rmjm/1181069346

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abstract = "We describe nonnegative weights on double struck T sign that are minimal at a given point and are related to quadrature identities for harmonic functions. The problem has a geometric interpretation in terms of a system of crescent regions carrying proportional harmonic measures. This system occurs as circle domains of a quadratic differential with second order poles. Our results have applications to harmonic polynomial approximation.",

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AB - We describe nonnegative weights on double struck T sign that are minimal at a given point and are related to quadrature identities for harmonic functions. The problem has a geometric interpretation in terms of a system of crescent regions carrying proportional harmonic measures. This system occurs as circle domains of a quadratic differential with second order poles. Our results have applications to harmonic polynomial approximation.

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KW - Polynomial approximation

KW - Quadratic differential

KW - Quadrature identity

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