PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 74 | 1 | 13-25
Tytuł artykułu

On extendability of invariant distributions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
74
Numer
1
Strony
13-25
Opis fizyczny
Twórcy
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv74z1p13bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.