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 |
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Pages (from-to) | 1819-1844 |
Number of pages | 26 |
Journal | Rocky Mountain Journal of Mathematics |
Volume | 36 |
Issue number | 6 |
DOIs | |
State | Published - 2006 |
Keywords
- Harmonic function
- Harmonic measure
- Polynomial approximation
- Quadratic differential
- Quadrature identity