\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Parametrices for the light ray transform on Minkowski spacetime

Abstract Full Text(HTML) Figure(1) Related Papers Cited by
  • We consider restricted light ray transforms arising from an inverse problem of finding cosmic strings. We construct a relative left parametrix for the transform on two tensors, which recovers the space-like and some light-like singularities of the two tensor.

    Mathematics Subject Classification: Primary: 53C65; Secondary: 35S30.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Illustration of complex $\mathscr{C}_0$

  •   J. Antoniano  and  G. Uhlmann , A functional calculus for a class of pseudodifferential operators with singular symbols, Proc. Symp. Pure Math., 43 (1985) , 5-16. 
      M. de Hoop , G. Uhlmann  and  A. Vasy , Diffraction from conormal singularities, Annales Scientifiques de l'École Normale Supérieure, 4e serie, 48 (2015) , 351-408.  doi: 10.24033/asens.2247.
      A. Greenleaf  and  A. Seeger , Fourier integral operators with fold singularities, J. reine angew. Math., 455 (1994) , 35-56. 
      A. Greenleaf  and  G. Uhlmann , Nonlocal inversion formulas for the X-ray transform, Duke Math. J., 58 (1989) , 205-240.  doi: 10.1215/S0012-7094-89-05811-0.
      A. Greenleaf  and  G. Uhlmann , Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms, Annales de l'institut Fourier, 40 (1990) , 443-466.  doi: 10.5802/aif.1220.
      A. Greenleaf  and  G. Uhlmann , Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, Journal of Functional Analysis, 89 (1990) , 202-232.  doi: 10.1016/0022-1236(90)90011-9.
      A. Greenleaf  and  G. Uhlmann , Microlocal techniques in integral geometry, Contemporary Mathematics, 113 (1990) , 121-135. 
      A. Greenleaf  and  G. Uhlmann , Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms. Ⅱ, Duke Math. J., 64 (1991) , 415-444.  doi: 10.1215/S0012-7094-91-06422-7.
      A. Greenleaf  and  G. Uhlmann , Recovering singularities of a potential from singularities of scattering data, Communications in Mathematical Physics, 157 (1993) , 549-572.  doi: 10.1007/BF02096882.
      V. Guillemin, Cosmology in $(2+1) $-Dimensions, Cyclic Models, and Deformations of $M_{2, 1} $ Annals of Mathematics Studies, No. 121, Princeton University Press, 1989.
      V. Guillemin  and  G. Uhlmann , Oscillatory integrals with singular symbols, Duke Math. J., 48 (1981) , 251-267.  doi: 10.1215/S0012-7094-81-04814-6.
      L. Hörmander , Fourier integral operators. Ⅰ, Acta Mathematica, 127 (1971) , 79-183.  doi: 10.1007/BF02392052.
      L. Hörmander, The Analysis of Linear Partial Differential Operators Ⅳ: Fourier Integral Operators Springer-Verlag, Berlin, Heidelberg, 2009.
      M. Lassas, L. Oksanen, P. Stefanov and G. Uhlmann, On the inverse problem of finding cosmic strings and other topological defects, preprint, arXiv: 1505.03123.
      R. Melrose  and  G. Uhlmann , Lagrangian intersection and the Cauchy problem, Communications on Pure and Applied Mathematics, 32 (1979) , 483-519.  doi: 10.1002/cpa.3160320403.
      B. Palacios , G. Uhlmann  and  Y. Wang , Reducing streaking artifacts in quantitative susceptibility mapping, SIAM Journal of Imaging Sciences, 10 (2017) , 1921-1934. 
      P. Stefanov, Support theorems for the light ray transform on analytic Lorentzian manifolds, Proc. Amer. Math. Soc., 145 (2017), 1259–1274. arXiv: 1504.01184.
  • 加载中

Figures(1)

SHARE

Article Metrics

HTML views(434) PDF downloads(209) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return