Front d'onde et propagation des singularités pour un vecteur-distribution

Dominique Manchon

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 2, page 161-191
  • ISSN: 0010-1354

Abstract

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We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.

How to cite

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Manchon, Dominique. "Front d'onde et propagation des singularités pour un vecteur-distribution." Colloquium Mathematicae 81.2 (1999): 161-191. <http://eudml.org/doc/210734>.

@article{Manchon1999,
abstract = {We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.},
author = {Manchon, Dominique},
journal = {Colloquium Mathematicae},
keywords = {wave front set; unitary representation; pseudo-differential-like operators},
language = {eng},
number = {2},
pages = {161-191},
title = {Front d'onde et propagation des singularités pour un vecteur-distribution},
url = {http://eudml.org/doc/210734},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Manchon, Dominique
TI - Front d'onde et propagation des singularités pour un vecteur-distribution
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 161
EP - 191
AB - We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.
LA - eng
KW - wave front set; unitary representation; pseudo-differential-like operators
UR - http://eudml.org/doc/210734
ER -

References

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  1. [Dui] J. J. Duistermaat, Fourier Integral Operators, Courant Institute, 1973 (Rééd. Progress in Math. 130, Birkhäuser, 1995). 
  2. [D-H] J. J. Duistermaat and L. Hörmander, Fourier integral operators II, Acta Math. 128 (1972), 183-269. Zbl0232.47055
  3. [Go] R. Goodman, Elliptic and subelliptic estimates for operators in an enveloping algebra, Duke Math. J. 47 (1980), 819-833. Zbl0466.35026
  4. [He] B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Astérisque 112 (1984). Zbl0541.35002
  5. [Hr1] L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), 359-443. Zbl0388.47032
  6. [Hr2] L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer, 1985. 
  7. [Hw] R. Howe, Wave front sets of representations of Lie groups, in: Automorphic Forms, Representation Theory and Arithmetic, Tata Inst. Fund. Res. Stud. Math. 10, Bombay, 1981, 117-140. 
  8. [Jο] P. E. T. Jοrgensen, Distribution representations of Lie groups, J. Math. Anal. Appl. 65 (1978), 1-19. 
  9. [M1] D. Manchon, Weyl symbolic calculus on any Lie group, Acta Appl. Math. 30 (1993), 159-186. Zbl0779.22005
  10. [M2] D. Manchon, Opérateurs pseudodifférentiels et représentations unitaires des groupes de Lie, Bull. Soc. Math. France 123 (1995), 117-138. 
  11. [M3] D. Manchon, Formule de Weyl pour les groupes de Lie nilpotents, J. Reine Angew. Math. 418 (1991), 77-129. Zbl0721.22004
  12. [M4] D. Manchon, Distributions à support compact et représentations unitaires, J. Lie Theory, à paraître. 
  13. [Me1] A. Melin, A remark on invariant pseudo-differential operators, Math. Scand. 30 (1972), 290-296. Zbl0258.22013
  14. [Me2] A. Melin, Parametrix constructions for right invariant differential operators on nilpotent groups, Ann. Global Anal. Geom. 1 (1983), 79-130. Zbl0524.58044
  15. [Ne] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. Zbl0091.10704
  16. [S] R. T. Seeley, Complex powers of an elliptic operator, in: Singular Integrals, Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 288-307. Zbl0159.15504
  17. [Shu] M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer, 1987. 
  18. [St] R. S. Strichartz, A functional calculus for elliptic pseudo-differential operators, Amer. J. Math. 94 (1972), 711-722. Zbl0246.35082
  19. [Stk] H. Stetkæ r, Invariant pseudo-differential operators, Math. Scand. 28 (1971), 105-123. 
  20. [T] M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, 1981 

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