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Linear analysis of quadrature domains. II
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-3125-3030
2000 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 119, 187-216 p.Article in journal (Refereed) Published
Abstract [en]

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 complement of a real affine ball is also investigated. Explicit computations on order-two quadrature domains illustrate the main results.

Place, publisher, year, edition, pages
2000. Vol. 119, 187-216 p.
URN: urn:nbn:se:kth:diva-20271ISI: 000166290100009OAI: diva2:338965
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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