A1 Journal article (refereed)
Applications of the Stone–Weierstrass theorem in the Calderón problem (2024)

Liimatainen, T., & Salo, M. (2024). Applications of the Stone–Weierstrass theorem in the Calderón problem. Annales Fennici Mathematici, 49(2), 583-600. https://doi.org/10.54330/afm.148911

JYU authors or editors

Publication details

All authors or editors: Liimatainen, Tony; Salo, Mikko

Journal or series: Annales Fennici Mathematici

ISSN: 2737-0690

eISSN: 2737-114X

Publication year: 2024

Publication date: 22/10/2024

Volume: 49

Issue number: 2

Pages range: 583-600

Publisher: Suomen matemaattinen yhdistys

Publication country: Finland

Publication language: English

DOI: https://doi.org/10.54330/afm.148911

Publication open access: Openly available

Publication channel open access: Open Access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/97852

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2404.01152

Abstract

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.

Keywords: partial differential equations; inverse problems

Free keywords: Calderón problem; density of products of solutions; Stone–Weierstrass theorem; plurisubharmonic function; transversally anisotropic manifold

Contributing organizations

Ministry reporting: Yes

VIRTA submission year: 2024

Preliminary JUFO rating: 2