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An L- L analog of miyachi's theorem for nilpotent lie groups and sharpness problems.
- Source :
-
Mathematical Notes . Jul2013, Vol. 94 Issue 1/2, p3-19. 17p. - Publication Year :
- 2013
-
Abstract
- The purpose of this paper is to formulate and prove an L- L analog of Miyachi's theorem for connected nilpotent Lie groups with noncompact center for 2 ≤ p, q ≤ +∞. This allows us to solve the sharpness problem in both Hardy's and Cowling-Price's uncertainty principles. When G is of compact center, we show that the aforementioned uncertainty principles fail to hold. Our results extend those of [1], where G is further assumed to be simply connected, p = 2, and q = +∞. When G is more generally exponential solvable, such a principle also holds provided that the center of G is not trivial. Representation theory and a localized Plancherel formula play an important role in the proofs. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE groups
*TOPOLOGICAL groups
*NILPOTENT groups
*MATHEMATICS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 94
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 89981151
- Full Text :
- https://doi.org/10.1134/S0001434613070018