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Minimizing functions for an uncertainty principle on locally compact groups of bounded representation dimension
Author(s):
Eberhard
Kaniuth
Journal:
Proc. Amer. Math. Soc.
135
(2007),
217-227.
MSC (2000):
Primary 43A30, 43A40
Posted:
June 29, 2006
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Abstract:
Let  be a locally compact group of bounded representation dimension  . Then, for any integrable function  on  , the product of the measures of the support of  and the support of its operator-valued Fourier transform on the dual space of  is bounded below by  . We classify all functions for which equality holds and prove criteria for when such functions exist.
References:
-
- 1.
- J. Dixmier,
 -algebras, North-Holland, Amsterdam, 1977.MR 0458185 (56:16388) - 2.
- D.L. Donoho and P.B. Stark, Uncertainty principles and signal discovery, SIAM J. Appl. Math. 49 (1989), 906-931. MR 0997928 (90c:42003)
- 3.
- S. Echterhoff and E. Kaniuth, Certain group extensions and twisted covariance algebras with generalized continuous trace, Lecture Notes in Math. 1359 (1988), 159-169. MR 0974312 (90c:46083)
- 4.
- G.B. Folland, A course in abstract harmonic analysis, CRC Press, Boca Raton, 1995.MR 1397028 (98c:43001)
- 5.
- W. Hauenschild and E. Kaniuth, Harmonische Analyse auf Gruppen mit endlich-dimensionalen irreduziblen Darstellungen, Math. Z. 144 (1975), 239-256.MR 0390125 (52:10951)
- 6.
- J.A. Hogan, A qualitative uncertainty principle for locally compact abelian groups, Miniconferences on harmonic analysis and operator algebras (Canberra 1987), Proc. Centre Math. Anal. Austral. Nat. Univ., Vol. 16 (1988), pp. 133-142.MR 0953989 (89k:43006)
- 7.
- J.A. Hogan, A qualitative uncertainty principle for unimodular groups of type I, Trans. Amer. Math. Soc. 340 (1993), 587-594. MR 1102222 (94b:43003)
- 8.
- A. Kleppner and R.L. Lipsman, The Plancherel formula for group extensions, Ann. Sci. Ec. Norm. Sup. 5 (1972), 459-516. MR 0342641 (49:7387)
- 9.
- G. Kutyniok, A weak qualitative uncertainty principle for compact groups, Illinois J. Math. 47 (2003), 709-724. MR 2007232 (2004h:43006)
- 10.
- G. Kutyniok, A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups, J. Math. Anal. Appl. 279 (2003), 580-596.MR 1974047 (2004d:43006)
- 11.
- T. Matolcsi and J. Szücs, Intersection des mesures spectrales conjugèes, C.R. Acad. Sci. Paris 277 (1973), 841-843. MR 0326460 (48:4804)
- 12.
- C.C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc. 166 (1972), 401-410. MR 0302817 (46:1960)
- 13.
- D.J.S. Robinson, Finiteness conditions and solvable groups. I, Springer, Berlin-Heidelberg-New York, 1972.
- 14.
- K.T. Smith, The uncertainty principle on groups, SIAM J. Appl. Math. 50 (1990), 876-882. MR 1050918 (91i:94008)
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Additional Information:
Eberhard
Kaniuth
Affiliation:
Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany
Email:
kaniuth@math.uni-paderborn.de
DOI:
10.1090/S0002-9939-06-08451-6
PII:
S 0002-9939(06)08451-6
Received by editor(s):
July 9, 2005
Received by editor(s) in revised form:
August 1, 2005
Posted:
June 29, 2006
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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