Publications and Preprints
Hart F. Smith
Recent Publications
(PDF format).
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Sharp local well-posedness results for the nonlinear wave equation.
Ann. of Math. (2) 162 (2005), 291-366.
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Spectral cluster estimates for C^{1,1} metrics .
Amer. Jour. Math. 128 (2006), 1069-1103.
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Sharp L^2-L^q bounds on spectral projectors for low regularity metrics .
Math. Res. Lett. 13 (2006), no.6, 967-974.
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On the L^p norm of spectral clusters for compact manifolds with boundary .
Acta Math. 198 (2007), 107-153.
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Sharp L^q bounds on spectral clusters for Holder metrics .
Math. Res. Lett. 14 (2007), no.1, 77-85.
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On Strichartz estimates for Schrodinger operators in compact manifolds
with boundary.
Proc. Amer. Math. Soc. 136 (2008), 247-256.
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On multilinear spectral cluster estimates for manifolds with boundary.
Math. Res. Lett. 15 (2008), 419-426.
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A multi-scale approach to hyperbolic evolution equations with
limited smoothness (8.4 MB).
Comm. Partial Differential Equations 33 (2008), 988-1017.
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Subcritical L^p bounds on spectral clusters for Lipschitz metrics .
Math. Res. Lett. 15 (2008), 993-1002.
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Seismic imaging with the generalized Radon transform: a curvelet transform perspective .
Inverse Problems 25 (2009), no. 2, 025005, 21 pp.
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Strichartz estimates for the wave equation on manifolds with boundary .
Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009), no.5, 1817-1829.
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On abstract Strichartz estimates and the Strauss conjecture for non-trapping obstacles .
Trans. Amer. Math. Soc. 362 (2010), no. 5, 2789-2809.
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Strichartz estimates and the nonlinear Schrodinger equation on manifolds with boundary .
Math. Ann. 354 (2012), 1397-1430.
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Decoupling of modes for the elastic wave equation in media of limited smoothness .
Comm. Partial Differential Equations 36 (2011), 1683-1693.
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Strichartz estimates for Dirichlet-wave equations in two dimensions with applications .
Trans. Amer. Math. Soc. 364 (2012), 3329-3347.
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Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data .
Math. Res. Lett. 19 (2012), 213-232.
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Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations of limited smoothness .
Appl. Comput. Harmon. Anal. 33 (2012), 330-353.
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Sharp bounds on spectral clusters for Lipschitz metrics . Amer. J. Math.
136 (2014), no. 6, 1629-1663.
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Pointwise bounds on quasimodes of semiclassical Schrodinger operators in dimension two . Math. Res. Lett. 20 (2013), 401-408.
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Propagation of singularities for rough metrics . Anal. PDE 7 (2014), no. 5, 1137-1178.
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Restriction bounds for the free resolvent and resonances in lossy scattering . arXiv:1401.6243. Int. Math. Res. Notices IMRN 2015, no. 16, 7473-7509.
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Heat traces and existence of scattering resonances for bounded potentials .
arXiv:1411.5420. Ann. Inst. Fourier (Grenoble) 66 (2016), no. 2, 455-475.
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On the trace of Schrodinger heat kernels and regularity of potentials .
Trans. Amer. Math. Soc. 371 (2019), no. 6, 3857-3875.
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Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature .
Pure Appl. Analysis 1 (2019), no. 1, 101-148.
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Parametrix for a semiclassical subelliptic operator .
Anal. PDE 7 (2020), no. 8, 2375-2398.
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Uniform resolvent estimates on manifolds of bounded curvature . Jour. Geom. Anal. 31 (2021), no. 7, 6766-6780.
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On the trace of the wave group and regularity of potentials . Submitted for publication.