Selected Publications of Tanya Christiansen

Home page of Tanya Christiansen

Selected Recent Papers (see also ArXived preprints):     
  • Inverse obstacle problems with backscattering or generalized backscattering data in one or two directions.  To appear, Asymptotic Analysis. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 1001156.
  • Schrodinger operators and the distribution of resonances in sectors.  To appear,  Analysis and PDE. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 1001156.
  • Resonances for manifolds hyperbolic at infinity: optimal lower bounds on order of growth (with D. Borthwick, P. D. Hislop, and P. Perry).  Int. Math. Research Notices (2011), no. 19, 4431-4470. 
    • Thanks to the NSF for partial support under grant DMS 1001156 and DMS 0500267.
  • Probabilistic Weyl laws for quantized tori (with M. Zworski). Comm. Math. Phys. 299 (2010), 305-334. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • A Mathematical formulation of the Mahaux-Weidenmuller formula for the scattering matrix (with M. Zworski).
    J. Phys. A: Math. Theor. 42 (2009) 415202. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Inverse problems for obstacles in a waveguide (with Michael Taylor).
    Comm. PDE 35, Issue 2 (2010) 328-352. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Maximal order of growth for the resonance counting functions for generic potentials in even dimensions (with P.D. Hislop).
    Ind. Univ. Math. J 59 (2010), 621-660 (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Resonances and balls in obstacle scattering with Neumann boundary condition.
    Inverse Probl. Imaging 2 (2008), no. 3, 335--340. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Sojourn times, manifolds with infinite cylindrical ends, and an inverse problem for planar waveguides.
    Journal d'Analyse Math. 107 (2009), 79--106. (PDF file)
    • The dvi file contains a figure that isn't in the PDF file.
    Thanks to the NSF for partial support under grant DMS 0500267.
  • Isophasal, isopolar, and isospectral Schr\"odinger operators and elementary complex analysis.
    Amer. J. Math. 130 (2008), no. 1, 49--58. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Several complex variables and the order of growth of the resonance counting function in Euclidean scattering.
    The final version (different from this (PDF file)) appeared in International Mathematics Research Notices. 12, (2006) Ariticle ID 43160, 1-36.
    • Thanks to the NSF for partial support under grant DMS 0500267.
  • Schr\"odinger operators with complex-valued potentials and no resonances.
    Duke Math Journal 12, 133, no. 2 (2006) 313-323. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0088922.
  • Resonances for steplike potentials: forward and inverse results.
    Trans. Amer. Math. Soc 12, 358 (2006), 2071-2089. (PDF file)
    • Thanks to the NSF for partial support under grant DMS 0088922.
  • The resonance counting function for Schr\"odinger operators with generic potentials (with P.D. Hislop).
    Math Research Letters, 12, (6) (2005), 821-826.
    Thanks to the NSF for partial support under grant DMS 0088922.
  • Asymptotics for a resonance-counting function for potential scattering on cylinders .
    Journal of Functional Analysis 216, No. 1 (2004), 172-190.
    Thanks to the NSF for partial support under grant DMS 0088922.
  • Pseudospectra in automorphic scattering (with M. Zworski).
    Forum Mathematicum 16, No. 5 (2004), 681-694.
    Thanks to the NSF for partial support under grant DMS 0088922.
  • Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations (with M.S. Joshi).
    Ann. Inst. Fourier 53, No. 2 (2003), 565-624.
    Thanks to the NSF for partial support under grant DMS 0088922.