Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An uncertainty principle on homogeneous trees

Author: Francesca Astengo
Journal: Proc. Amer. Math. Soc. 131 (2003), 3155-3161
MSC (2000): Primary 43A85; Secondary 22E35
Published electronically: April 1, 2003
MathSciNet review: 1992856
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathfrak{X}$ be a homogeneous tree of degree $q+1$. We prove an uncertainty principle in this setting regarding ``exponentially decreasing'' functions on trees whose Fourier transforms have a ``deep zero''.

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

  • 1. F. Astengo, M. Cowling, B. Di Blasio, and M. Sundari, Hardy's Uncertainty Principle on certain Lie groups, J. London Math. Soc. 62 (2000), 461-472. MR 2002b:22018
  • 2. W. Betori and M. Pagliacci, The Radon transform on trees, Boll. Un. Mat. Ital. 5-B (1986), 267-277. MR 87h:05073
  • 3. M. G. Cowling, S. Meda and A. G. Setti, An overview of harmonic analysis on the group of isometries of a homogeneous tree, Exposition. Math. 16 (1998), 385-423. MR 2000i:43005
  • 4. M. G. Cowling, S. Meda and A. G. Setti, Estimates for functions of the Laplace operator on homogeneous trees, Trans. Amer. Math. Soc. 352 (2000), 4271-4293. MR 2000m:43005
  • 5. A. Figà-Talamanca and C. Nebbia, Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, London Math. Soc. Lecture Notes Series, 162, Cambridge Univ. Press, Cambridge, 1991. MR 93f:22004
  • 6. A. Figà-Talamanca and M. Picardello, Harmonic Analysis on Free Groups, Dekker, New York, 1983. MR 85j:43001
  • 7. G. B. Folland and A. Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl. 3 (1997), 207-238. MR 98f:42006
  • 8. E. K. Narayanan and S. K. Ray, $L^p$ versions of Hardy's theorem on semisimple groups, Proc. Amer. Math. Soc. 130 (2002), 1859-1866. MR 2003a:22009
  • 9. V. Havin and B. Jöricke, The Uncertainty Principle in Harmonic Analysis, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 28, Springer-Verlag, Berlin, 1994. MR 96c:42001
  • 10. S. Thangavelu, Hardy's Theorem for the Helgason Fourier transform on noncompact rank one symmetric spaces, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A85, 22E35

Retrieve articles in all journals with MSC (2000): 43A85, 22E35

Additional Information

Francesca Astengo
Affiliation: Dipartimento di Matematica, Università di Genova, 16146 Genova, Italia

Received by editor(s): May 6, 2002
Published electronically: April 1, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society