Convexity for invariant differential operators on semisimple symmetric spaces

E. P. Van den Ban; H. Schlichtkrull

Compositio Mathematica (1993)

  • Volume: 89, Issue: 3, page 301-313
  • ISSN: 0010-437X

How to cite


Van den Ban, E. P., and Schlichtkrull, H.. "Convexity for invariant differential operators on semisimple symmetric spaces." Compositio Mathematica 89.3 (1993): 301-313. <>.

author = {Van den Ban, E. P., Schlichtkrull, H.},
journal = {Compositio Mathematica},
keywords = {invariant differential operator; convexity; reductive symmetric space},
language = {eng},
number = {3},
pages = {301-313},
publisher = {Kluwer Academic Publishers},
title = {Convexity for invariant differential operators on semisimple symmetric spaces},
url = {},
volume = {89},
year = {1993},

AU - Van den Ban, E. P.
AU - Schlichtkrull, H.
TI - Convexity for invariant differential operators on semisimple symmetric spaces
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 89
IS - 3
SP - 301
EP - 313
LA - eng
KW - invariant differential operator; convexity; reductive symmetric space
UR -
ER -


  1. [1] E van den Ban: A convexity theorem for semisimple symmetric spaces, Pac. J. Math.124 (1986), 21-55. Zbl0599.22014MR850665
  2. [2] E van den Ban: Asymptotic behaviour of matrix coefficients related to reductive symmetric spaces, Proc. Kon. Nederl. Akad. Wet90 (1987), 225-249. Zbl0629.43008MR914083
  3. [3] E. van den Ban and H. Schlichtkrull: The most continuous part of the Plancherel decomposition for a reductive symmetric space. In preparation. Zbl0878.43018
  4. [4] E. van den Ban and H. Schlichtkrull: Multiplicities in the Plancherel decomposition for a semisimple symmetric space. In (R. L. Lipsman e.a. eds) Representation Theory of Groups and Algebras, Contemp. Math., Vol. 145, p. 163-180. Amer. Math. Soc., Providence1993. Zbl0809.43004MR1216188
  5. [5] A. Cérézo and F. Rouvière: Opérateurs différentiels invariants sur un groupe de Lie, Sém. Goulaouic-Schwartz 1972-73 (1973), Exposé X, p. X.1-X.9. Zbl0259.58012MR430153
  6. [6] W. Chang: Global solvability of the Laplacians on pseudo-Riemannian symmetric spaces, J. Funct. Anal.34 (1979), 481-492. Zbl0431.58015MR556268
  7. [7] W. Chang: Invariant differential operators and P-convexity of solvable Lie groups, Adv. in Math.46 (1982), 284-304. Zbl0506.22012MR683203
  8. [8] J. Dadok: Solvability of invariant differential operators of principal type on certain Lie groups and symmetric spaces, J. d'Anal. Math.37 (1980), 118-127. Zbl0445.58031MR583634
  9. [9] M. Duflo and D. Wigner: Convexité pour les operateurs différentiels invariants sur les groupes de Lie, Math. Zeit.167 (1979), 61-80. Zbl0387.43007MR532886
  10. [10] M. Flensted-Jensen: Spherical functions on a real semisimple Lie group. A method of reduction to the complex case, J. Funct. Anal.30 (1978), 106-146. Zbl0419.22019MR513481
  11. [11] M. Flensted-Jensen: Analysis on Non-Riemannian Symmetric Spaces, Regional Conference Series in Math. 61, Amer. Math. Soc., Providence1986. Zbl0589.43008MR837420
  12. [12] Harish-Chandra: Spherical functions on a semisimple Lie group, I, Amer. J. Math.80 (1958), 241-310. Zbl0093.12801MR94407
  13. [13] S. Helgason: Fundamental solutions of invariant differential operators on symmetric spaces, Amer. J. Math.86 (1964), 565-601. Zbl0178.17001MR165032
  14. [14] S. Helgason: The surjectivity of invariant differential operators on symmetric spaces I, Ann. of Math.98 (1973), 451-479. Zbl0274.43013MR367562
  15. [15] S. Helgason: Groups and Geometric Analysis, Academic Press, Orlando1984. Zbl0543.58001MR754767
  16. [16] S. Helgason: Invariant differential operators and Weyl group invariants. In (W. Barker and P. Sally, eds.) Harmonic Analysis on Reductive Groups, Bowdoin College1989, Birkhäuser, Boston1991, p. 193-200. Zbl0760.43002MR1168483
  17. [17] L. Hörmander: Linear Partial Differential Operators, Springer Verlag, Berlin1963. Zbl0108.09301
  18. [18] T. Oshima and J. Sekiguchi: Eigenspaces of invariant differential operators on a semisimple symmetric space, Invent. Math.57 (1980), 1-81. Zbl0434.58020MR564184
  19. [19] J. Rauch and D. Wigner: Global solvability of the Casimir operators, Ann. of Math.103 (1976), 229-236. Zbl0323.58021MR425017
  20. [20] F. Rouvière: Invariant differential equations on certain semisimple Lie groups, Trans. Amer. Math. Soc.243 (1978), 97-114. Zbl0399.58023MR502896
  21. [21] H. Schlichtkrull: Harmonic Analysis on Symmetric Spaces, Birkhäuser, Boston1984. MR757178
  22. [22] F. Treves: Linear Partial Differential Equations, Gordon and Breach, New York1970. Zbl0209.12001
  23. [23] O. Zariski and P. Samuel: Commutative Algebra, Vol. I, Van Nostrand, Princeton1958. Zbl0121.27801MR90581

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.