ArticleOriginal scientific text

Title

On extendability of invariant distributions

Authors

Abstract

In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature.

Keywords

Hausdorff partition, foliation, invariant distribution

Bibliography

  1. O. V. Besov et al., Integral Representations of Functions and Imbedding Theorems, Nauka, Moscow, 1975 (in Russian).
  2. G. E. Bredon, Introduction to Compact Transformation Groups, Academic Press, 1972.
  3. A. Cerezo, Equations with constant coefficients invariant under a group of linear transformations, Trans. Amer. Math. Soc. 204 (1975), 267-298.
  4. V. Edén, Disributions invariant under the group of complex orthogonal transformations, Math. Scand. 14 (1964), 75-89.
  5. C. Herz, Invariant distributions, in: Proc. Sympos. Pure Math. 35, Part 2, Amer. Math. Soc., 1979, 361-373.
  6. P. Jeanquartier, Distributions et opérateurs différentiels homogènes et inva- riants, Comment. Math. Helv. 39 (1965), 205-252.
  7. S. Łojasiewicz, Ensembles semi-analytiques, IHES, 1965.
  8. B. Malgrange, Ideals of Differentiable Functions, Oxford Univ. Press, 1966.
  9. P.-D. Methée, Sur les distributions invariantes dans le groupe des rotations de Lorentz, Comment. Math. Helv. 28 (1954), 225-269.
  10. R. Narasimhan, Analysis on Real and Complex Manifolds, Masson, Paris, 1968.
  11. A. I. Oksak, On invariant and covariant Schwartz distributions in the case of a compact linear group, Comm. Math. Phys. 46 (1976), 269-287.
  12. G. de Rham, Sur la division de formes et de courants par une forme linéaire, Comment. Math. Helv. 28 (1954), 346-352.
  13. L. Schwartz, Séminaire 1954/55, Exposé n°7.
  14. G. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63-68.
  15. A. Tengstrand, Distributions invariant under an orthogonal group of arbitrary signature, Math. Scand. 8 (1960), 201-218.
  16. H. Weyl, The Classical Groups, Princeton Univ. Press, 1946.
  17. B. Ziemian, On G-invariant distributions, J. Differential Equations 35 (1980), 66-86.
  18. B. Ziemian, Distributions invariant under compact Lie groups, Ann. Polon. Math. 42 (1983), 175-183.
  19. Yu. M. Zinoviev, On Lorentz invariant distributions, Comm. Math. Phys. 47 (1976), 33-42.
Pages:
13-25
Main language of publication
English
Published
2000
Exact and natural sciences