Proceedings of the Japan Academy, Series A, Mathematical Sciences

An uncertainty principle on Sturm-Liouville hypergroups

Radouan Daher and Takeshi Kawazoe

Full-text: Open access

Abstract

As an analogue of the classical uncertainty inequality on the Euclidean space, we shall obtain a generalization on the Sturm-Liouville hypergroups $(\mathbf{R}_{+},*(A))$. Especially, we shall obtain a condition on $A$ under which the discrete part of the Plancherel formula vanishes.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 9-10 (2007), 167-169.

Dates
First available in Project Euclid: 22 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1201012599

Digital Object Identifier
doi:10.3792/pjaa.83.167

Mathematical Reviews number (MathSciNet)
MR2376598

Zentralblatt MATH identifier
1143.43005

Subjects
Primary: 43A62: Hypergroups 43A32: Other transforms and operators of Fourier type 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
uncertainty principle Sturm-Liouville hypergroup

Citation

Daher, Radouan; Kawazoe, Takeshi. An uncertainty principle on Sturm-Liouville hypergroups. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 9-10, 167--169. doi:10.3792/pjaa.83.167. https://projecteuclid.org/euclid.pja/1201012599


Export citation

References

  • W. R. Bloom and H. Heyer, Harmonic analysis of probability measures on hypergroups, de Gruyter, Berlin, 1995.
  • O. Bracco, Fonction maximale associée à des opérateurs de Sturm-Liouville singuliers, Thèse, Univ. Louis Pasteur, Strasbourg, 1999.
  • T. Kawazoe, Uncertainty principles for the Jacobi transforms, Tokyo J. Math. (to appear).