Quadrature domains packing
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912128626065408 |
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| author | Gustafsson, Bjorn Putinar, Mihai |
| author_facet | Gustafsson, Bjorn Putinar, Mihai |
| contents | Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument analytic/anti-analytic kernel defined in a neighborhood of infinity. In case the compact sets are closures of quadrature domains the respective kernel is rational, enabling an effective matrix analysis algorithm for the non-overlapping decision. The simplest situation of two disks is presented in detail from a matrix model perspective as well as from a Riemann surface potential theoretic interpretation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadrature domains packing Gustafsson, Bjorn Putinar, Mihai Spectral Theory Complex Variables 47B20, 30F15, 31A05, 52C15, 86A22 Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument analytic/anti-analytic kernel defined in a neighborhood of infinity. In case the compact sets are closures of quadrature domains the respective kernel is rational, enabling an effective matrix analysis algorithm for the non-overlapping decision. The simplest situation of two disks is presented in detail from a matrix model perspective as well as from a Riemann surface potential theoretic interpretation. |
| title | Quadrature domains packing |
| topic | Spectral Theory Complex Variables 47B20, 30F15, 31A05, 52C15, 86A22 |
| url | https://arxiv.org/abs/2411.14124 |