arXiv math/03063242003-06-23math.CVmath.AC

Ullemar's formula for the Jacobian of the complex moment mapping

Olga S. Kuznetsova, Vladimir G. Tkachev

备注：: 14 pages, submitted for "Complex Variables. Theory and Application"
发表信息：: Complex Variables and Elliptic Equations, Volume 49, Issue 1 January 2004, pages 55 - 72
DOI：: 10.1080/02781070310001634610

英文摘要：

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.

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