Linear analysis of quadrature domains. II
2000 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 119, 187-216 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:kth:diva-20271ISI: 000166290100009OAI: oai:DiVA.org:kth-20271DiVA: diva2:338965
QC 201005252010-08-102010-08-10Bibliographically approved