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Atomization process for convolution operators on locally compact groups


Author: Cédric Delmonico
Journal: Proc. Amer. Math. Soc. 134 (2006), 3231-3241
MSC (2000): Primary 43A05; Secondary 43A22, 47B38, 47B48
DOI: https://doi.org/10.1090/S0002-9939-06-08345-6
Published electronically: May 12, 2006
MathSciNet review: 2231906
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Abstract: We develop for a large class of locally compact groups a method of approximation of convolution operators on $ G$ by finitely supported measures with control of the support and of the operator norm of the approximating measures.


References [Enhancements On Off] (What's this?)

  • 1. Jean-Philippe Anker, Applications de la $ p$-induction en analyse harmonique, Comment. Math. Helv. 58 (1983), no. 4, 622-645. MR 0728457 (85c:22006)
  • 2. David L. Armacost, The structure of locally compact abelian groups, Monographs and Textbooks in Pure and Applied Mathematics, vol. 68, Marcel Dekker, Inc., New York, 1981. MR 0637201 (83h:22010)
  • 3. Jacques Delaporte and Antoine Derighetti, $ p$-pseudomeasures and closed subgroups, Monatsh. Math. 119 (1995), no. 1-2, 37-47. MR 1315682 (97a:43001)
  • 4. Cédric Delmonico, Opérateurs de convolution et homomorphismes de groupes localement compacts., Ph.D. thesis, Université de Lausanne, 2003.
  • 5. Antoine Derighetti, Relations entre les convoluteurs d'un groupe localement compact et ceux d'un sous-groupe fermé, Bull. Sci. Math. (2) 106 (1982), no. 1, 69-84. MR 0654425 (83j:43008)
  • 6. Carl Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 91-123. MR0355482 (50:7956)
  • 7. Noël Lohoué, Sur le critère de S. Bochner dans les algèbres $ B\sb{p}\,(R\sp{n})$ et l'approximation bornée des convoluteurs, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A247-A250. MR 0273300 (42:8180)
  • 8. -, Algèbres $ {A}\sb p(G)$ et convoluteurs de $ L^p(G)$, Doctorat d'état, Université Paris-Sud, Centre d'Orsay, 1971.
  • 9. -, La synthèse des convoluteurs sur un groupe abélien localement compact, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A27-A29. MR 0275062 (43:820)
  • 10. Hans Reiter and Jan D. Stegeman, Classical harmonic analysis and locally compact groups, second ed., The Clarendon Press, Oxford University Press, New York, 2000. MR 1802924 (2002d:43005)
  • 11. Kenneth A. Ross and Karl Stromberg, Jessen's theorem on Riemann sums for locally compact groups, Pacific J. Math. 20 (1967), 135-147. MR 0207889 (34:7702)
  • 12. Jose L. Rubio, Nets of subgroups in locally compact groups, Comment. Math. Prace Mat. 20 (1977/78), no. 2, 453-466. MR 0519384 (80c:43002)

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Additional Information

Cédric Delmonico
Affiliation: School of Basic Sciences, École Polytechnique Fédérale de Lausanne, Station 8, CH-1005 Lausanne, Switzerland
Email: cedric.delmonico@a3.epfl.ch

DOI: https://doi.org/10.1090/S0002-9939-06-08345-6
Keywords: Convolution operators, discrete measures, approximations, dense nets
Received by editor(s): February 3, 2005
Received by editor(s) in revised form: May 17, 2005
Published electronically: May 12, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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