Minimal kernels, quadrature identities and proportional harmonic measures

John R. Akeroyd, Kristi Karber, Alexander Yu Solynin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish
Pages (from-to)1819-1844
Number of pages26
JournalRocky Mountain Journal of Mathematics
Issue number6
StatePublished - 2006


  • Harmonic function
  • Harmonic measure
  • Polynomial approximation
  • Quadratic differential
  • Quadrature identity


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