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Selected topics on quadrature domains Bjorn Gustafsson a

Summary: Selected topics on quadrature domains
Bjšorn Gustafsson a
aDepartment of Mathematics, Royal Institute of Technology, Stockholm S-100 44,
Mihai Putinar b
bDepartment of Mathematics, University of California, Santa Barbara, CA 93106
This is a selection of facts, old and new, about quadrature domains. The text, writ-
ten in the form of a survey, is addressed to non-experts and covers a variety of phe-
nomena related to quadrature domains. Such as: the difference between quadrature
domains for subharmonic, harmonic and respectively complex analytic functions,
geometric properties of the boundary, instability in the reverse Hele-Shaw flow, de-
pendence and non-uniqueness on the quadrature data, interpretation in terms of
function theory on Riemann surfaces, a matrix model and a reconstruction algo-
rithm. Plus some low degree/order examples where computations can be carried
out in detail.
Key words: Quadrature domain, potential, free boundary, Markov moment
problem, principal function
1 Introduction
Finite nodes, Gaussian type quadratures are traditionally constructed for poly-


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics