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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
Posted:
May 12, 2006
MathSciNet review:
2231906
Full-text PDF Free Access
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Abstract: We develop for a large class of locally compact groups a method of approximation of convolution operators on  by finitely supported measures with control of the support and of the operator norm of the approximating measures.
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Anker, Applications de la 𝑝-induction en analyse
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(83h:22010)
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Delaporte and Antoine
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(97a:43001), http://dx.doi.org/10.1007/BF01292767
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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
(French, with English summary). MR 654425
(83j:43008)
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Lohoué, Sur le critère de S. Bochner dans les
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(French). MR
0273300 (42 #8180)
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-, Algèbres
 et convoluteurs de  , Doctorat d'état, Université Paris-Sud, Centre d'Orsay, 1971.
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A-B 272 (1971), A27–A29 (Russian). MR 0275062
(43 #820)
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Hans
Reiter and Jan
D. Stegeman, Classical harmonic analysis and locally compact
groups, 2nd ed., London Mathematical Society Monographs. New Series,
vol. 22, The Clarendon Press Oxford University Press, New York, 2000.
MR
1802924 (2002d:43005)
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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)
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Jose
L. Rubio, Nets of subgroups in locally compact groups,
Comment. Math. Prace Mat. 20 (1977/78), no. 2,
453–466. MR
519384 (80c:43002)
- 1.
- Jean-Philippe Anker, Applications de la
 -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,
 -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
 et l'approximation bornée des convoluteurs, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A247-A250. MR 0273300 (42:8180)
- 8.
- -, Algèbres et convoluteurs de , 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:
http://dx.doi.org/10.1090/S0002-9939-06-08345-6
PII:
S 0002-9939(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
Posted:
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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