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 | |
| State | Published - Dec 1 2006 |
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Keywords
- Harmonic function
- Harmonic measure
- Polynomial approximation
- Quadratic differential
- Quadrature identity
Cite this
Akeroyd, J. R., Karber, K., & Solynin, A. Y. (2006). Minimal kernels, quadrature identities and proportional harmonic measures. Rocky Mountain Journal of Mathematics, 36(6), 1819-1844. https://doi.org/10.1216/rmjm/1181069346