Plamen D Stefanov
Publications of Plamen Stefanov
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Existence of the scattering operator for dissipative hyperbolic systems with variable multiplicities (with V. Georgiev), J. Operator Theory 19(1988), 217-241.
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Spectral and scattering theory for the linear Boltzmann equation in exterior domain, Math. Nachr. 137(1988), 63-77.
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Inverse scattering problem for the wave equation with time dependent potential, J. Math. Anal. Appl.140(1989), 351-362.
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Uniqueness of the inverse scattering problem for the wave equation with a potential depending on time, Inverse Prob. 4(1988), 913-920.
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The Newton-Marchenko equation for time-dependent potentials, Inverse Prob. 4(1988), 921-928.
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Uniqueness of the three-dimensional inverse scattering problem for time-dependent potentials, Inverse Prob. 5(1989), L11-L14.
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Uniqueness of the multi-dimensional inverse scattering problem for time-dependent potentials, Math. Z. 201(1989), 541-559.
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A uniqueness result for the inverse back-scattering problem, Inverse Prob. 6(1990), 1055-1064.
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Inverse scattering problem for moving obstacles, Math. Z. 207(1991), 461-480.
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Stability of the inverse problem in potential scattering at fixed energy, Ann. Inst. Fourier, Grenoble 40(1990), 867-884.
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Generic uniqueness for two inverse problems in potential scattering, Comm. P.D.E. 17(1992), 55-68.
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Fixed energy inverse scattering for non-compactly supported potentials (with A. G. Ramm), Math. & Comput. Modeling 18(1993), 57-64.
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Stability of the resonances under smooth perturbations of the boundary, Asympt. Anal. 9(1994), 291-296.
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Distribution of resonances for the Neumann problem in linear elasticity outside a ball (with G. Vodev), Ann. Inst. Henry Poincaré (Phys. Théorique) 60(3)(1994), 303-321.
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Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body (with G. Vodev), Duke Math. J. 78(1995), 577-714.
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Inverse scattering and inverse boundary value problems for the linear Boltzmann equation (with M. Choulli), Comm. P.D.E. 21(5&6)(1996), 763-785.
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Neumann resonances in linear elasticity for an arbitrary body (with G. Vodev), Comm. Math. Phys. (1996), 645-659.
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Scattering theory with two L1 spaces: application to transport equations with obstacles (with M. Chabi and M. Mokhtar-Kharroubi), Ann. Fac. Sci. Toulouse 6(3)(1997), 511-523.
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Inverse backscattering for the acoustic equation (with G. Uhlmann), SIAM J. Math. Anal. 28(5)(1997), 1191-1204.
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Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media (with G. Uhlmann), J. Funct. Anal.154(2)(1998), 330-358.
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Rigidity for metrics with the same lengths of geodesics (with G. Uhlmann), Math. Res. Lett. 5(1998), 83-96.
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An inverse boundary value problem for the stationary transport equation (with M. Choulli), Osaka J. Math. 36(1)(1999), 87-104.
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Quasimodes and resonances: sharp lower bounds, Duke Math. J. 99(1999), 75-92.
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Lower bound of the number of the Rayleigh resonances for arbitrary body, Indiana Univ. Math. J. 49(2)(2000), 405-426.
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Resonances near the real axis imply existence of quasimodes, C. R. Acad. Sci. Paris, Serie I 330(2)(2000), 105-108.
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Resonance expansions and Rayleigh waves, Math. Res. Lett. 8(1-2)(2001), 105-124.
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Weyl type upper bounds on the number of resonances near the real axis for trapped systems, Journées Equations aux Dérivées Partielles, Plestin-les-gréves, 5-8 juin 2001, Exposé No. XIII.
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Estimates on the residue of the scattering amplitude, Asymptotic Anal. 32(3-4)(2002), 317-333.
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Sharp upper bounds on the number of resonances near the real axis for trapping systems, Amer. J. Math. 125(1)(2003), 183-224.
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Resonance expansions of propagators in the presence of potential barriers (with Shu Nakamura and Maciej Zworski), J. Funct. Anal. 205(2003), 180-205.
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Optical Tomography in two dimensions (with Gunther Uhlmann), Methods Appl. Anal. 10(1)(2003), 1-9.
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Inverse problems in transport theory, in Inside Out: Inverse Problems and Applications, MSRI Publications, Vol. 47, 2003.
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Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering (with Gunther Uhlmann), Proc. Amer. Math. Soc. 132(2004), 1351-1354.
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Stability estimates for the X-ray transform of tensor fields and boundary rigidity (with Gunther Uhlmann), Duke Math. J. 123(2004), 445-467.
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Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map (with Gunther Uhlmann), IMRN 17(2005), 1047-1061.
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Recent Progress on the Boundary Rigidity Problem (with Gunther Uhlmann), Electron. Res. Announc. Amer. Math. Soc. 11(2005), 64-70.
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Boundary rigidity and stability for generic simple metrics (with Gunther Uhlmann), Journal Amer. Math. Soc. 18(2005), 975-1003.
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Approximating resonances with the Complex Absorbing Potential Method, Commun. PDE, 30(2005), 1843-1862.
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Sharp upper bounds on the number of the scattering poles, J. Funct. Anal. 231(1)(2006), 111-142.
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The boundary rigidity problem in the presence of a magnetic field (with Nurlan Dirbekov, Gabriel Paternain and Gunther Uhlmann), Adv. Math. 216(2)(2007), 535-609.
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Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity, Serdica Math. J., 34(1)(2008), 67-112. An extended version of the mini-course I gave at the Symposium on Inverse Problems, Rio de Janeiro, Jan. 2007.
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The X-Ray transform for a generic family of curves and weights, with Bela Frigyik and Gunther Uhlmann, J. Geom. Anal. 18(1)(2008), 81-97.
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Integral geometry of tensor fields on a class of non-simple Riemannian manifolds (with Gunther Uhlmann), Amer. J. Math. 130(1)(2008), 239-268.
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Boundary and Lens Rigidity, Tensor Tomography and Analytic Microlocal Analysis (with Gunther Uhlmann), in Algebraic Analysis of Differential Equations, Fetschrift in Honor of Takahiro Kawai, edited by T. Aoki, H. Majima, Y. Katei and N. Tose, pp. 275-293 (2008).
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A sharp stability estimate in tensor tomography, J. of Physics: Conference Series, (Vol 124: Proceeding of the First International Congress of the IPIA), 124(2008), 012007.
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An inverse source problem in optical molecular imaging (with Gunther Uhlmann), Analysis & PDE, 1(1)(2008), 115-126.
Recent Publications (newest on the bottom)
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Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds, (with Gunther Uhlmann), J. Diff. Geom. 82(2)(2009), 383-409.
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Linearizing non-linear inverse problems and an application to inverse backscattering (with Gunther Uhlmann), J. Funct. Anal. 256(9)(2009), 2842-2866.
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Uniqueness and non-uniqueness in inverse radiative transfer, (with Alexandru Tamasan), Proc. Amer. Math. Soc. 137(2009), 2335-2344.
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A support theorem for the geodesic ray transform of symmetric tensor fields (with Venky Krishnan), Inverse Problems and Imaging 3(3), (2009) 453-464.
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Thermoacoustic tomography with variable sound speed (with Gunther Uhlmann), Inverse Prob. 25(2009), 075011.
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The weighted Doppler transform (with Sean Holman), Inverse Problems and Imaging, 4(1)(2010), 111-130.
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Stability of the gauge equivalent classes in stationary Inverse Transport (with Stephen McDowall and Alexandru Tamasan), Inverse Prob. 26(2010), 025006.
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Gauge equivalence in stationary radiative transport through media with varying index of refraction (with Stephen McDowall and Alexandru Tamasan), Inverse Problems and Imaging, 4(1), (2010), 151-167.
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Stability of the gauge equivalent classes in inverse stationary transport in refractive media (with Stephen McDowall and Alexandru Tamasan), Contemporary Math., 559(2011), 85-100.
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Thermoacoustic tomography arising in brain imaging (with Gunther Uhlmann), Inverse Prob. 27(2011), 045004.
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An efficient Neumann-series based algorithm for Thermoacoustic and Photoacoustic Tomography with variable sound speed (with Jianliang Qian, Gunther Uhlmann and Hongkai Zhao), SIAM J. Imaging Sciences, 4(2011), 850-883.
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The geodesic X-ray transform with fold caustics (with Gunther Uhlmann), Analysis & PDE, 5-2 (2012), 219-260.
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Recovery of a source term or a speed with one measurement and applications (with Gunther Uhlmann), to appear in Trans. AMS.
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Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data (with Mourad Choulli), Commun. PDE, 38(3)(2013), 455-476.
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Is a curved flight path in SAR better than a straight one? (with Gunther Uhlmann) to appear in SIAM J. Appl. Math.
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Multi-wave methods via ultrasound (with Gunther Uhlmann), in Inside Out II, MSRI publications, 60, 2012, 271-324.
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The Identification Problem for the attenuated X-ray transform, submitted.
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Instability of the linearized problem in multiwave tomography of recovery both the source and the speed (with Gunther Uhlmann).
Recent Talks, Lecture Notes and a unfinished book project
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Recovering Anisotropic Metrics from Travel Times, a plenary talk at the First International Congress of IPIA. Conference on Applied Inverse Problems 2007: Theoretical and Computational Aspects
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An inverse source problem in optical molecular imaging, talk at the Summer School on Inverse Problems in Radiative Transfer, UC Merced, June 2008.
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Traveltime Tomography and Tensor Tomography, MSRI, July 2009, lecture notes. Lecture 1, Lectures 2&3, Lecture 4.
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Thermoacoustic and Photoacoustic Tomography with a variable continuous or discontinuous sound speed, MSRI, November 2010.
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Mini-course I on Microlocal methods in TAT, Fields Institute: Lecture 1 (Uniqueness), Lecture 2&3 (Microlocal stuff), Lecture 4 (Stability and Partial data), Lecture 5 ("brain imaging"). Pictures and movies that I showed, all created by Francois Monard.
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Mini-course II on Microlocal methods in X-ray tomography, Fields Institute, 2012: Lecture 1 (the Euclidean case), Lecture 2&3 (Microlocal stuff)
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Microlocal Analysis and Integral Geometry, a book project with Gunther Uhlmann, still in infancy.
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Scattering, Inverse Scattering and Resonances, graduate course lecture notes, work in progress.
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Is a curved flight path in SAR better than a straight one?, talk I gave at Stanford, 2012.
My current students: Carlos Montalto, Andrew Homan.
Most of the publications have been supported by NSF.
Last updated on April 10, 2013