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Linear analysis of quandrature domains. II

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Abstract

The natural correspondence between bounded planar quadrature domains, in the terminology of Aharonov-Shapiro, and certain square matrices with a distinguished cyclic vector is further exploited. Two different cubature formulas on quadrature domains, that is the computation of the integral of a real polynomial, are presented. The minimal defining polynomial of a quadrature domain is decomposed uniquely into a linear combination of moduli squares of complex polynomials. The geometry of a canonical rational embedding of a quadrature domain into the projective complemnt of a real affine ball is also investigated. Explicit computations on order-two quadrature domains illustrate the main results.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden

    Björn Gustafsson

  2. Department of Mathematics, University of California, 93117, Santa Barbara, CA, USA

    Mihai Putinar

Authors
  1. Björn Gustafsson
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  2. Mihai Putinar
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Paper partially supported by the National Science Foundation Grant DMS-95000954.

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Gustafsson, B., Putinar, M. Linear analysis of quandrature domains. II. Isr. J. Math. 119, 187–216 (2000). https://doi.org/10.1007/BF02810668

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  • DOI: https://doi.org/10.1007/BF02810668

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