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.