1 citations · 1 across the 7 of their papers we have counts for
7 papers
On Constrained Riesz Minimum Energy Problems
Dan Coroian, Peter Dragnev, Alan Legg +1
The constrained equilibrium problem for the logarithmic potential was introduced by Rakhmanov (1996) as he realized that the asymptotic distribution of the zeros of discrete orthog…
Ellipses and Polynomial-to-Polynomial Mapping of Weighted Szego Projections
Alan R. Legg
We take a look at weighted Szego projections on ellipses and ellipsoids in light of some known results of real and complex potential theory. We show that on planar ellipses there i…
Point Source Equilibrium Problems with Connections to Weighted Quadrature Domains
Peter D. Dragnev, Alan R. Legg, Edward B. Saff
We explore the connection between supports of equilibrium measures and quadrature identities, especially in the case of point sources added to the external field wi…
On the Best Uniform Polynomial Approximation to the Checkmark Function
Peter D. Dragnev, Alan R. Legg, Ramon Orive
The best uniform polynomial approximation of the checkmark function is considered, as varies in . For each fixed degree , the minimax error is…
Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges
A. R. Legg, P. D. Dragnev
With the sphere as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the eq…
Mapping Properties of Quadrature Domains in Several Complex Variables
Alan R. Legg
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomor…
The Khavinson-Shapiro Conjecture for the Bergman Projection in One and Several Complex Variables
Alan R. Legg
We reveal a complex analogue to a result about polynomial solutions to the Dirichlet Problem on ellipsoids in by showing that the Bergman projection on any ellipsoid…