Applications of the Stone-Weierstrass theorem in the Calderón problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916187929051136 |
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| author | Liimatainen, Tony Salo, Mikko |
| author_facet | Liimatainen, Tony Salo, Mikko |
| contents | We give examples on the use of the Stone-Weierstrass theorem in inverse problems. We show uniqueness in the linearized Calderón problem on holomorphically separable Kähler manifolds, and in the Calderón problem for nonlinear equations on conformally transversally anisotropic manifolds. We also study the holomorphic separability condition in terms of plurisubharmonic functions. The Stone-Weierstrass theorem allows us to generalize and simplify earlier results. It also makes it possible to circumvent the use of complex geometrical optics solutions and inversion of explicit transforms in certain cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of the Stone-Weierstrass theorem in the Calderón problem Liimatainen, Tony Salo, Mikko Complex Variables Analysis of PDEs Differential Geometry 35R30, 35J25, 35J61 We give examples on the use of the Stone-Weierstrass theorem in inverse problems. We show uniqueness in the linearized Calderón problem on holomorphically separable Kähler manifolds, and in the Calderón problem for nonlinear equations on conformally transversally anisotropic manifolds. We also study the holomorphic separability condition in terms of plurisubharmonic functions. The Stone-Weierstrass theorem allows us to generalize and simplify earlier results. It also makes it possible to circumvent the use of complex geometrical optics solutions and inversion of explicit transforms in certain cases. |
| title | Applications of the Stone-Weierstrass theorem in the Calderón problem |
| topic | Complex Variables Analysis of PDEs Differential Geometry 35R30, 35J25, 35J61 |
| url | https://arxiv.org/abs/2404.01152 |