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1999 | 81 | 2 | 161-191
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
81
Numer
2
Strony
161-191
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-16
poprawiono
1998-12-07
Twórcy
  • Institut Elie Cartan, Université Henri Poincaré, CNRS - INRIA BP 239, 54506 Vandœ uvre-lès-Nancy Cedex, France
Bibliografia
  • [Dui] J. J. Duistermaat, Fourier Integral Operators, Courant Institute, 1973 (Rééd. Progress in Math. 130, Birkhäuser, 1995).
  • [D-H] J. J. Duistermaat and L. Hörmander, Fourier integral operators II, Acta Math. 128 (1972), 183-269.
  • [Go] R. Goodman, Elliptic and subelliptic estimates for operators in an enveloping algebra, Duke Math. J. 47 (1980), 819-833.
  • [He] B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Astérisque 112 (1984).
  • [Hr1] L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), 359-443.
  • [Hr2] L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer, 1985.
  • [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.
  • [Jο] P. E. T. Jοrgensen, Distribution representations of Lie groups, J. Math. Anal. Appl. 65 (1978), 1-19.
  • [M1] D. Manchon, Weyl symbolic calculus on any Lie group, Acta Appl. Math. 30 (1993), 159-186.
  • [M2] D. Manchon, Opérateurs pseudodifférentiels et représentations unitaires des groupes de Lie, Bull. Soc. Math. France 123 (1995), 117-138.
  • [M3] D. Manchon, Formule de Weyl pour les groupes de Lie nilpotents, J. Reine Angew. Math. 418 (1991), 77-129.
  • [M4] D. Manchon, Distributions à support compact et représentations unitaires, J. Lie Theory, à paraître.
  • [Me1] A. Melin, A remark on invariant pseudo-differential operators, Math. Scand. 30 (1972), 290-296.
  • [Me2] A. Melin, Parametrix constructions for right invariant differential operators on nilpotent groups, Ann. Global Anal. Geom. 1 (1983), 79-130.
  • [Ne] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615.
  • [S] R. T. Seeley, Complex powers of an elliptic operator, in: Singular Integrals, Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 288-307.
  • [Shu] M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer, 1987.
  • [St] R. S. Strichartz, A functional calculus for elliptic pseudo-differential operators, Amer. J. Math. 94 (1972), 711-722.
  • [Stk] H. Stetkæ r, Invariant pseudo-differential operators, Math. Scand. 28 (1971), 105-123.
  • [T] M. E. Taylor, Pseudodifferential Operators, Princeton Univ. Press, 1981
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv81i2p161bwm
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