Wiener type algebras of pseudodifferential operators

J. Sjöstrand

Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995)

  • page 1-19

How to cite


Sjöstrand, J.. "Wiener type algebras of pseudodifferential operators." Séminaire Équations aux dérivées partielles (Polytechnique) (1994-1995): 1-19. <>.

author = {Sjöstrand, J.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Hörmander’s class; Wiener lemma; Gårding inequality},
language = {eng},
pages = {1-19},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Wiener type algebras of pseudodifferential operators},
url = {},
year = {1994-1995},

AU - Sjöstrand, J.
TI - Wiener type algebras of pseudodifferential operators
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1994-1995
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 19
LA - eng
KW - Hörmander’s class; Wiener lemma; Gårding inequality
UR -
ER -


  1. [Be] R. Beals, Characterization of P.D.O. and applications, Duke math. J.44(1977), 45-57. Zbl0353.35088MR435933
  2. [B] J.M. Bony, Opérateurs intégraux de Fourier et calcul de Weyl-Hörmander. (Cas d'une métrique symplectique), Proceedings of the "Journées d'équations aux dérivées partielles"St Jean de Monts, 30 mai- 3 juin 1994. Ecole Polytechnique, Université de Nantes, Université de Rennes 1 MR1298680
  3. [CF] A. Cordoba, C. Fefferman, Wave packets and Fourier integral operators, Comm. P.D.E.3(11)(1978), 979-1006. Zbl0389.35046MR507783
  4. [GriS] A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, London Math. Soc. Lect. Notes Series 196, Cambridge Univ. Press (1994). Zbl0804.35001MR1269107
  5. [GraSch] B. Gramsch, E. Schrohe, Submultiplicativity of Boutet de Monvel's algebra for boundary value problems, Preprint Max-Planck-Institut für MathematikBonn (1994). Zbl0823.46050MR1287668
  6. [GraUeW] B. Gramsch, J. Ueberberg, K. Wagner, Spectral invariance and submultiplicativity for Fréchet algebras with applications to pseudodifferential operators and Ψ*-quantization, pages 71-98 in "Operator calculus and spectral theory", Symposium on operator calculus and spectral theory, Lambrecht (Germany), December 1991, Ed. by M.Demuth..., Birkhäuser1992, Operator theory, Vol. 57. Zbl0900.35450
  7. [HeS] B. Helffer, J. Sjöstrand, Analyse semi-classique pour l'équation de Harper. Bull. de la SMF, 116(4)(1988), mémoire no 34. Zbl0714.34130
  8. [H1] L. Hörmander, The analysis of linear partial differential operators, I-IV, Grundlehren, Springer, 256, 257, 274, 275 (1983-85). Zbl0521.35001MR717035
  9. [H2] L. Hörmander, Quadratic hyperbolic operators, Springer L.N.M., 1495 (1991), 118-160. Zbl0761.35004MR1178557
  10. [KN] J.J. Kohn, L. Nirenberg, On the algebra of pseudo-differential operators, Comm. Pure Appl. Math.18(1965), 269-305. Zbl0171.35101MR176362
  11. [LKa] P.G. Lemarié-Rieusset, J.P. Kahane, Book to appear, chapter 10. 
  12. [Lo] L. Loomis, An introduction to abstract harmonic analysis, Van Nostrand, Toronto, New York, London, (1953). Zbl0052.11701MR54173
  13. [Sh] M.S. Shubin, Almost periodic functions and partial differential equations, Uspechi Math. Nauk33(2)(1978), 243-275, Russian Math. Surveys33(2)(1978), 1-52. Zbl0408.47039
  14. [S1] J. Sjöstrand, An algebra of pseudodifferential operators, Math. Res. Lett.1(1994),185-192. Zbl0840.35130MR1266757
  15. [S2] J. Sjöstrand, Unpublished lecture notes from Lund (1985- 86). 
  16. [S3] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, 95(1982). Zbl0524.35007MR699623
  17. [T] M. Taylor, Pseudodifferential operators, Princeton Univ. Press (1981). Zbl0453.47026MR618463
  18. [U] A. Unterberger, Les opérateurs métadifférentiels, Lecture Notes in Physics, 126(1980), 205-241. Zbl0452.35121MR579751
  19. [Z] A. Zygmund, Trigonometric series, Cambridge Univ. Press, 2nd edition (1959). See vol. 1, page 246 and note on page 380. Zbl0367.42001MR107776

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.