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. Go to preprint in arXiv

  • 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. Go to preprint in arXiv

  • 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. Go to preprint in arXiv

    Schroedinger equation

  • A. Hassell and J. Wunsch, The semiclassical resolvent and the propagator for nontrapping scattering metrics, Advances in Mathematics 217 (2008), 586-682. Go to preprint in arXiv ; Go to journal

  • A. Hassell, T. Tao and J. Wunsch, Sharp Strichartz estimates on non-trapping asymptotically conic manifolds, American Journal of Mathematics, 128 (2006), 963-1024. Go to preprint in arXiv

  • 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. Go to preprint in arXiv

  • A. Hassell and J. Wunsch, The Schroedinger propagator for scattering metrics, Annals of Mathematics, 162 (2005), 487-523. Go to preprint in arXiv

  • A. Hassell and J. Wunsch, On the structure of the Schroedinger propagator, Contemp. Math. 362, 2004. Conference paper. Go to preprint in 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. Go to preprint in arXiv

  • A. Hassell, L. Hillairet and J. Marzuola, Eigenfunction concentration for polygonal billiards. Communications in PDE, to appear. Go to preprint in 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. Go to preprint in arXiv

  • N. Burq, A. Hassell and J. Wunsch, Spreading of quasimodes in the Bunimovich stadium, Proc. Amer. Math. Soc 135 (2007), 1029-1037. Go to preprint in arXiv

  • A. Hassell and S. Zelditch, Quantum ergodicity of boundary values of eigenfunctions, Communications in Mathematical Physics, 248, 119-168, 2004. Go to preprint in arXiv

  • A. Hassell and T. Tao, Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions. Math. Res. Lett. 9 (2002), 289-307. Go to preprint in 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. Download pdf file

    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. Go to preprint in arXiv

  • 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. Go to preprint in arXiv

  • 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. Go to preprint in arXiv

  • 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. Download ps 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. Download ps file Go to preprint in arXiv

  • 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. Download ps file Go to preprint in arXiv

  • A. Hassell and M. Zworski, Resonant rigidity of S^2, J. Funct. Anal. 169, 604-609 (1999). Reprints available. Download ps file

    Quantum N body problem

  • A. Hassell, Distorted plane waves for the 3 body Schroedinger operator, Geometric and Functional Analysis 10, 1-50 (2000). Download ps file

  • A. Hassell and A. Vasy, Symbolic functional calculus and N body resolvent estimates, Journal of Functional Analysis 173, 257-283, 2000. Reprints available. Download ps file

  • A. Hassell, Scattering matrices for the quantum N body problem, Transactions of the AMS 352 (2000), 3799-3820. Reprints available. Download ps file

    Spectral invariants

  • A. Hassell and S. Zelditch, Determinants of Laplacians in exterior domains, IMRN, 1999, number 18, 971-1004. Reprints available. Download ps file Go to preprint in arXiv

  • A. Hassell, Analytic surgery and analytic torsion, Commun. in Anal. and Geom. 6, 255-289 (1998). Reprints available. Download ps file

  • 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. Download ps file Go to preprint in arXiv

  • A. Hassell, The Yang-Mills-Higgs Heat Flow on R^3, J. Funct. Anal. 111, 431-448, 1993. Reprints available.