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pro vyhledávání: '"Jathar, Shubham R."'
Autor:
Jathar, Shubham R., Railo, Jesse
The article surveys inverse problems related to the twisted geodesic flows on Riemannian manifolds with boundary, focusing on the generalized ray transforms, tensor tomography, and rigidity problems. The twisted geodesic flow generalizes the usual ge
Externí odkaz:
http://arxiv.org/abs/2410.04911
Autor:
Jathar, Shubham R., Railo, Jesse
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
Comment: 7 pages, 11 figures, accepted survey article
Comment: 7 pages, 11 figures, accepted survey article
Externí odkaz:
http://arxiv.org/abs/2410.04908
The momentum ray transform $I_m^k$ integrates a rank $m$ symmetric tensor field $f$ on ${\mathbb R}^n$ over lines with the weight $t^k$, $I_m^kf(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,\mathrm{d}t$. Let $N^k_m=(I^k_m)^*I^k_m$
Externí odkaz:
http://arxiv.org/abs/2408.08085
Publikováno v:
The Journal of Fourier Analysis and Applications 30, 58 (2024)
The momentum ray transform $I_m^k$ integrates a rank $m$ symmetric tensor field $f$ on $\mathbb R^n$ over lines with the weight $t^k$, $I_m^kf(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,\mathrm{d}t$. We compute the normal operato
Externí odkaz:
http://arxiv.org/abs/2401.00791
We study the injectivity of the matrix attenuated and nonabelian ray transforms on compact surfaces with boundary for nontrapping $\lambda$-geodesic flows and the general linear group of invertible complex matrices. We generalize the loop group facto
Externí odkaz:
http://arxiv.org/abs/2312.06023
Publikováno v:
The Journal of Geometric Analysis 34, 212 (2024)
We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have nonpositive
Externí odkaz:
http://arxiv.org/abs/2306.17604
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