222 research outputs found
Topology of quadrature domains
We address the problem of topology of quadrature domains, namely we give
upper bounds on the connectivity of the domain in terms of the number of nodes
and their multiplicities in the quadrature identity.Comment: 37 pages, 11 figures in J. Amer. Math. Soc., Published
electronically: May 11, 201
Planar Orthogonal Polynomials As Type II Multiple Orthogonal Polynomials
We show that the planar orthogonal polynomials with logarithmic
singularities in the potential are the multiple orthogonal polynomials
(Hermite-Pad\'e polynomials) of Type II with measures. We also find the
ratio between the determinant of the moment matrix corresponding to the
multiple orthogonal polynomials and the determinant of the moment matrix from
the original planar measure
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