Anders Christian Hansen


Junior Research Fellow

Department of Applied Mathematics and Theoretical Physics
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Rd
Cambridge CB3 0WA
United Kingdom

Telephone +44 1223 760403
Email A.Hansen [at] damtp.cam.ac.uk

Research Interests

Functional Analysis (applied), Operator/Spectral theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory,
Computational Harmonic Analysis, Inverse Problems, Complexity Theory, Geometric Integration, Numerical Analysis, C*-algebras

Papers

    2011
  1. B. Adcock & A. C. Hansen & E. Herrholz & G. Teschke, "Generalized sampling, infinite-dimensional compressed sensing, and semi-random sampling for asymptotically incoherent dictionaries".
  2. B. Adcock & A. C. Hansen & E. Herrholz & G. Teschke, "Generalized Sampling: Extensions to Frames and Ill-Posed Problems".
  3. B. Adcock & A. C. Hansen, "Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients".
  4. B. Adcock & A. C. Hansen, "Sharp bounds, optimality and a geometric interpretation for generalised sampling in Hilbert spaces".
  5. B. Adcock & A. C. Hansen, "Reduced Consistency Sampling in Hilbert Spaces", Proceedings of the 9th International Conference on Sampling Theory and Applications
  6. B. Adcock & A. C. Hansen, "Generalized Sampling and Infinite Dimensional Compressed Sensing".
    7. 2010
  7. A. C. Hansen & C. Wong, "On the computation of spectra and pseudospectra of self-adjoint and non-self-adjoint Schrodinger operators".
  8. A. C. Hansen & O. Nevanlinna, "Complexity Issues in Computing Spectra, Pseudospectra and Resolvents", Banach Center Publ. (to appear)
  9. B. Adcock & A. C. Hansen, "Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon", Appl. Comput. Harmon. Anal. (to appear)
  10. B. Adcock & A. C. Hansen, "A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases", J. Fourier Anal. Appl. (to appear)
    11. 2009
  11. A. C. Hansen, "A theoretical framework for backward error analysis on manifolds", J. Geom. Mech. 3, no. 1, 81 - 111
  12. A. C. Hansen, "On the Solvability Complexity Index, the n-Pseudospectrum and Approximations of Spectra of Operators", J. Amer. Math. Soc. 24, no. 1, 81-124
    13. 2008
  13. A. C. Hansen, "The infinite dimensional QR-algorithm".
  14. A. C. Hansen & J. Strain, "On the order of deferred correction", Appl. Numer. Math. 61, no. 8, 961-973
  15. A. C. Hansen, "Infinite dimensional numerical linear algebra; theory and applications", Proc. R. Soc. Lond. Ser. A. 466, no. 2124, 3539-3559
  16. A. C. Hansen, "On the approximation of spectra of linear operators on Hilbert spaces", J. Funct. Anal. 254, no. 8, 2092--2126
  17. A. C. Hansen & J. Strain, "Convergence theory for spectral deferred correction", Preprint, UC Berkeley

Thesis

  1. A. C. Hansen,"On the approximation of spectra of linear Hilbert space operators", PhD Thesis.

Awards

  1. Smith-Knight/Rayleigh-Knight Prize 2007, "On the approximation of spectra and pseudospectra of linear operators on Hilbert spaces"
  2. John Butcher Award 2007 (joint with T. Schmelzer (Oxford)), "A theoretical framework for backward error analysis on manifolds".

CV

    CV