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

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

2003-06-23

arxiv.org/abs/math/0306324v1

Complex Variables and Elliptic Equations, Volume 49, Issue 1 January 2004, pages 55 - 72

Mathematics

Complex Variables

14 pages, submitted for "Complex Variables. Theory and Application"

Scientific paper

10.1080/02781070310001634610

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.

Affiliated with

Also associated with

No associations

Rating

Ullemar's formula for the Jacobian of the complex moment mapping does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ullemar's formula for the Jacobian of the complex moment mapping, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ullemar's formula for the Jacobian of the complex moment mapping will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513736