Geodesic
Applications of the Stone–Weierstrass theorem in the Calderón problem
Tony Liimatainen1 ; Mikko Salo2
1University of Helsinki, Department of Mathematics and Statistics
2University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 583–600

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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.
DOI : 10.54330/afm.148911
Keywords: Calderón problem, density of products of solutions, Stone–Weierstrass theorem, plurisubharmonic function, transversally anisotropic manifold

Tony Liimatainen  1   ; Mikko Salo  2

1 University of Helsinki, Department of Mathematics and Statistics
2 University of Jyväskylä, Department of Mathematics and Statistics 
Tony Liimatainen; Mikko Salo. Applications of the Stone–Weierstrass theorem in the Calderón problem. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 583–600. doi: 10.54330/afm.148911
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