Pseudospectrum for differential operators

Johannes Sjöstrand[1]

  • [1] CMAT, Ecole Polytechnique, FR-91128 Palaiseau cedex, and UMR 7640, CNRS

Séminaire Équations aux dérivées partielles (2002-2003)

  • Volume: 2002-2003, page 1-9

How to cite


Sjöstrand, Johannes. "Pseudospectrum for differential operators." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-9. <>.

affiliation = {CMAT, Ecole Polytechnique, FR-91128 Palaiseau cedex, and UMR 7640, CNRS},
author = {Sjöstrand, Johannes},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {non-selfadjoint operators; resolvent; review; Weyl asymptotics},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Pseudospectrum for differential operators},
url = {},
volume = {2002-2003},
year = {2002-2003},

AU - Sjöstrand, Johannes
TI - Pseudospectrum for differential operators
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 9
LA - eng
KW - non-selfadjoint operators; resolvent; review; Weyl asymptotics
UR -
ER -


  1. J. Bokobza, A. Unterberger, Les opérateurs pseudodifférentiels d’ordre variable, C.R.A.S. Paris 261(1965), 2271–2273. Zbl0143.37003
  2. E. B. Davies, Non-selfadjoint differential operators, Bull. London Math. Soc. 34(5)(2002), 513–532. Zbl1052.47042MR1912874
  3. E. B. Davies, Semi-classical states for non-self-adjoint Schrödinger operators, Comm. Math. Phys., 200(1999), 35–41. Zbl0921.47060MR1671904
  4. N. Dencker, J. Sjöstrand, M. Zworski, Pseudospectra of semi-classical (pseudo)differential operators, Comm. P. Appl. Math., to appear. Zbl1054.35035
  5. M. Hager, Thèse, In preparation. 
  6. B. Helffer, J. Sjöstrand, Résonances en limite semi-classique, Mémoires de la S.M.F. 114(3)(1986). Zbl0631.35075MR871788
  7. L. Hörmander, The analysis of linear partial differential operators, I–IV, Springer verlag 1983–1985. Zbl0521.35001
  8. L. Hörmander, Differential operators of principal type, Math. Ann. 140(1960), 124–146; Differential equations without solutions, Math. Ann. 140(1960), 169–173. Zbl0090.08101MR130574
  9. M. Kashiwara, T. Kawai, Microhyperbolic pseudo-differential operators, I, J. Math. Soc. Japan 27(1975), 359–404. Zbl0305.35066MR377998
  10. A. Martinez, Resonance free domains for non globally analytic potentials, Ann. Henri Poincaré 4(2002), 739–756. Zbl1026.81012MR1933368
  11. M. Sato, T. Kawai, M. Kashiwara, Microfunctions and pseudo-differential equations. Hyperfunctions and pseudo-differential equations pp. 265–529. Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973. Zbl0277.46039MR420735
  12. L.N. Trefethen, S.J. Chapman, Wave packet pseudomodes of twisted Toeplitz matrices, preprint (2002). Zbl1055.15014MR2059680
  13. A. Unterberger, Résolution d’équations aux dérivées partielles dans des espaces de distributions d’ordre variable, Ann. Inst. Fourier, 21(2)(1971), 85–128. Zbl0205.43104
  14. M. Zworski, A remark on a paper by E.B. Davies, Proc. A.M.S., 129(2001), 2955-2957. Zbl0981.35107MR1840099
  15. M. Zworski, Numerical linear algebra and solvability of partial differential equations, Comm. Math. Phys. 229(2002), 293–307. Zbl1021.35077MR1923176

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.