On operators satisfying the Rockland condition

Waldemar Hebisch

Studia Mathematica (1998)

  • Volume: 131, Issue: 1, page 63-71
  • ISSN: 0039-3223

Abstract

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Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.

How to cite

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Hebisch, Waldemar. "On operators satisfying the Rockland condition." Studia Mathematica 131.1 (1998): 63-71. <http://eudml.org/doc/216563>.

@article{Hebisch1998,
abstract = {Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.},
author = {Hebisch, Waldemar},
journal = {Studia Mathematica},
keywords = {Rockland condition; regular kernel; homogeneous Lie group; Schwartz class function; operator},
language = {eng},
number = {1},
pages = {63-71},
title = {On operators satisfying the Rockland condition},
url = {http://eudml.org/doc/216563},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Hebisch, Waldemar
TI - On operators satisfying the Rockland condition
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 1
SP - 63
EP - 71
AB - Let G be a homogeneous Lie group. We prove that for every closed, homogeneous subset Γ of G* which is invariant under the coadjoint action, there exists a regular kernel P such that P goes to 0 in any representation from Γ and P satisfies the Rockland condition outside Γ. We prove a subelliptic estimate as an application.
LA - eng
KW - Rockland condition; regular kernel; homogeneous Lie group; Schwartz class function; operator
UR - http://eudml.org/doc/216563
ER -

References

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  2. [2] M. Christ, D. Geller, P. Głowacki and L. Pollin, Pseudodifferential operators on groups with dilations, Duke Math. J. 68 (1992), 31-65. Zbl0764.35120
  3. [3] R. Coifman et G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971. Zbl0224.43006
  4. [4] R. Coifman et G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., Providence, 1977. Zbl0371.43009
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  9. [9] P. Głowacki, The Rockland condition for nondifferential convolution operators, Duke Math. J. 58 (1989), 371-395. Zbl0678.43002
  10. [10] P. Głowacki, The Rockland condition for nondifferential convolution operators II, Studia Math. 98 (1991), 99-114. Zbl0737.43002
  11. [11] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe gradué, Comm. Partial Differential Equations 3 (1978), 889-958. Zbl0423.35040
  12. [12] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), 235-244. Zbl0564.43007
  13. [13] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspekhi Mat. Nauk 17 (4) (1962), 57-110 (in Russian). 
  14. [14] J. Nourrigat, Inégalités L 2 et représentations de groupes nilpotents, J. Funct. Anal. 74 (1987), 300-327. Zbl0644.35026
  15. [15] J. Nourrigat, L 2 inequalities and representations of nilpotent groups, C.I.M.P.A. School of Harmonic Analysis, Wuhan, to appear. Zbl0644.35026

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