Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Mönkkönen, Keijo"'
Autor:
Ilmavirta, Joonas, Mönkkönen, Keijo
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to t
Externí odkaz:
http://arxiv.org/abs/2203.16886
Autor:
Mönkkönen, Keijo
This is the introductory part of my PhD thesis on inverse problems arising in medical and seismic imaging. The topics include X-ray tomography of scalar and vector fields with partial data, higher order fractional Calder\'on problems, travel time tom
Externí odkaz:
http://arxiv.org/abs/2107.02615
Autor:
Ilmavirta, Joonas, Mönkkönen, Keijo
We prove that if $P(D)$ is some constant coefficient partial differential operator and $f$ is a scalar field such that $P(D)f$ vanishes in a given open set, then the integrals of $f$ over all lines intersecting that open set determine the scalar fiel
Externí odkaz:
http://arxiv.org/abs/2103.14385
Autor:
Mönkkönen, Keijo
If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics
Externí odkaz:
http://arxiv.org/abs/2010.11484
Publikováno v:
Journal of Inverse and Ill-posed Problems, vol. 31, no. 1, 2023, pp. 43-63
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on ten
Externí odkaz:
http://arxiv.org/abs/2009.01043
Publikováno v:
Advances in Mathematics 399 (2022), 108246
We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order of the fractional Laplacian. We show that one can uniquely recover t
Externí odkaz:
http://arxiv.org/abs/2008.10227
Autor:
Ilmavirta, Joonas, Mönkkönen, Keijo
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray tra
Externí odkaz:
http://arxiv.org/abs/2006.05790
Publikováno v:
Inverse Problems & Imaging, 2021, 15 (4): 641-681
We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq 0$. We apply the results
Externí odkaz:
http://arxiv.org/abs/2001.06210
Autor:
Ilmavirta, Joonas, Mönkkönen, Keijo
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique continuation property in the class of compactly supported distributions. This immediately implies uniqueness for the X-ray tomography problem with part
Externí odkaz:
http://arxiv.org/abs/1909.05585
Publikováno v:
In Advances in Mathematics 16 April 2022 399
