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

Access to Document

10.1216/rmjm/1181069346

Cite this

@article{cf5b9450961c433695bef12f15a54acb,

title = "Minimal kernels, quadrature identities and proportional harmonic measures",

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.",

keywords = "Harmonic function, Harmonic measure, Polynomial approximation, Quadratic differential, Quadrature identity",

author = "Akeroyd, {John R.} and Kristi Karber and Solynin, {Alexander Yu}",

year = "2006",

doi = "10.1216/rmjm/1181069346",

language = "English",

volume = "36",

pages = "1819--1844",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

number = "6",

}

TY - JOUR

T1 - Minimal kernels, quadrature identities and proportional harmonic measures

AU - Akeroyd, John R.

AU - Karber, Kristi

AU - Solynin, Alexander Yu

PY - 2006

Y1 - 2006

N2 - 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.

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.

KW - Harmonic function

KW - Harmonic measure

KW - Polynomial approximation

KW - Quadratic differential

KW - Quadrature identity

UR - http://www.scopus.com/inward/record.url?scp=34247273058&partnerID=8YFLogxK

U2 - 10.1216/rmjm/1181069346

DO - 10.1216/rmjm/1181069346

M3 - Article

AN - SCOPUS:34247273058

VL - 36

SP - 1819

EP - 1844

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 6

ER -

Minimal kernels, quadrature identities and proportional harmonic measures

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this