Dr. Andrew Hassell
Reader
Department of Mathematics
Australian National University
Canberra ACT 0200 Australia
Email: hassell {AT} maths.anu.edu.au
Fax: (61) (2) 6125 4984
Phone: (61) (2) 6125 4141
Publications, listed by topic
Low energy asymptotics of the resolvent and Riesz transform
A. Hassell and A.Sikora,
Riesz transforms in one dimension. Indiana Journal, to appear.
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C. Guillarmou and A. Hassell,
Resolvent at low energy and Riesz transform
for Schr\"odinger operators on asymptotically conic manifolds. II. Annales de l'Institut Fourier, to appear.
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C. Guillarmou and A. Hassell,
Resolvent at low energy and Riesz transform
for Schr\"odinger operators on asymptotically conic manifolds. I, Math. Annalen, 341 (2008), no. 4, 859--896.
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Schroedinger equation
A. Hassell and J. Wunsch, The semiclassical resolvent and the propagator for nontrapping scattering metrics, Advances in Mathematics 217 (2008), 586-682.
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A. Hassell, T. Tao and J. Wunsch, Sharp Strichartz estimates on
non-trapping asymptotically conic manifolds, American Journal of Mathematics, 128 (2006), 963-1024.
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A. Hassell, T. Tao and J. Wunsch, A Strichartz inequality for the
Schroedinger equation on non-trapping asymptotically conic manifolds,
Communications in PDE 30(2005), 157-205.
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A. Hassell and J. Wunsch, The Schroedinger propagator for scattering metrics,
Annals of Mathematics, 162 (2005), 487-523.
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arXiv
A. Hassell and J. Wunsch, On the structure of the Schroedinger propagator, Contemp. Math. 362, 2004. Conference paper.
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arXiv
Asymptotics of eigenfunctions and eigenvalues
A. Hassell, Ergodic billiards that are not quantum unique ergodic. With an
appendix by A. Hassell and L. Hillairet. Annals of Mathematics, to appear.
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arXiv
A. Hassell, L. Hillairet and J. Marzuola, Eigenfunction concentration for polygonal billiards. Communications in PDE, to appear.
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arXiv
A. Hassell and S. Marshall, Eigenvalues of Schroedinger operators with potential
asymptotically homogeneous of degree -2, Trans. Amer. Math. Soc 360 (2008), no. 8, 4145--4167.
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arXiv
N. Burq, A. Hassell and J. Wunsch, Spreading of quasimodes in the Bunimovich stadium,
Proc. Amer. Math. Soc 135 (2007), 1029-1037.
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A. Hassell and S. Zelditch, Quantum ergodicity of boundary values of eigenfunctions,
Communications in Mathematical Physics, 248, 119-168, 2004.
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A. Hassell and T. Tao, Upper and lower bounds for normal derivatives of Dirichlet
eigenfunctions. Math. Res. Lett. 9 (2002), 289-307.
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arXiv
A. Hassell and T. Tao, L^ 2 bounds for normal derivatives of Dirichlet eigenfunctions, Proc. Centre Math. Appl. Austral. Nat. Univ., 41, 57 -- 67, 2003. Conference paper.
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Scattering Theory and Operator Kernels
A. Hassell, R. B. Melrose and A. Vasy,
Microlocal propagation near
radial points and scattering for symbolic potentials of order zero, Analysis and PDE 1 (2008), 127-196.
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G. Carron, T. Coulhon and A. Hassell,
Riesz transform and L^p cohomology for manifolds with Euclidean ends. Duke Math. J., 133 (2006), 59-93.
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A. Hassell, R. B. Melrose and A. Vasy,
Spectral and scattering theory for symbolic potentials of order
zero, Advances in Mathematics 181(2004), 1-87.
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A. Hassell, R. B. Melrose and A. Vasy, Spectral and scattering theory
for symbolic potentials of order zero. Seminaire:
Equations aux Derivees Partielles, 2000--2001,
Exp. No. XIII, 21 pp., Semin. Equ. Deriv. Partielles, Ecole
Polytech., Palaiseau, 2001.
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file. Conference paper.
A. Hassell and A. Vasy, The resolvent for Laplace-type operators on
asymptotically conic spaces. Ann. l'Inst. Fourier 51 (2001), 1299-1346.
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file
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A. Hassell and A. Vasy, The spectral projections and resolvent
for scattering metrics,
Journal d'Analyse Mathematique 79 (1999), 241-298.
With Andras Vasy. Reprints available.
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file
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A. Hassell and M. Zworski, Resonant rigidity of S^2,
J. Funct. Anal. 169, 604-609 (1999).
Reprints available.
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Quantum N body problem
A. Hassell, Distorted plane waves for the 3 body Schroedinger operator,
Geometric and Functional Analysis 10, 1-50 (2000).
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A. Hassell and A. Vasy, Symbolic functional calculus and N body resolvent estimates,
Journal of Functional Analysis 173, 257-283, 2000. Reprints available.
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A. Hassell, Scattering matrices for the quantum N body problem, Transactions
of the AMS 352 (2000), 3799-3820. Reprints available.
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Spectral invariants
A. Hassell and S. Zelditch, Determinants of Laplacians in exterior domains,
IMRN, 1999, number 18, 971-1004.
Reprints available.
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file
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A. Hassell, Analytic surgery and analytic torsion,
Commun. in Anal. and Geom. 6,
255-289 (1998). Reprints available.
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A. Hassell, R. Mazzeo and R. B. Melrose, A signature theorem for
manifolds with corners of codimension two, Topology 36, 1055-1075, 1997. Reprints
available.
A. Hassell, R. Mazzeo and R. B. Melrose, Analytic surgery and the
accumulation of eigenvalues, Commun. in Anal. and Geom. 3, 115-222, 1995. Reprints
available.
Miscellaneous papers in spectral theory and PDE
A. Hassell and A. Vasy, Intersecting Legendrians and blowups.
Mathematical Research Letters 8 (2001), 413-428.
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arXiv
A. Hassell, The Yang-Mills-Higgs Heat Flow on R^3,
J. Funct. Anal. 111, 431-448, 1993. Reprints available.
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