Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T03:55:09.837Z Has data issue: false hasContentIssue false
  • English
  • Français

Functional Equations and Fourier Analysis

Published online by Cambridge University Press:  20 November 2018

Dilian Yang
Dilian Yang*
Affiliation:
Department of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations — the d'Alembert equation, the Wilson equation, and the d'Alembert long equation — on compact groups.

Keywords

39B5222C0543A30functional equationsFourier analysisrepresentation of compact groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 218 - 224
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] An, J. and Yang, D., A Levi-Civitá equation on compact groups and nonabelian Fourier analysis. Integral Equations Operator Theory 66 (2010), no. 2, 183–195. http://dx.doi.org/10.1007/s00020-010-1740-8 Google Scholar
[2] An, J. and Yang, D., Nonabelian harmonic analysis and functional equations on compact groups. J. Lie Theory 21 (2011), no. 2, 427–456.Google Scholar
[3] Akkouchi, M., Bouikhalene, B., and Elqorachi, E., Functional equations and μ-spherical functions. Georgian Math. J. 15 (2008), no. 1, 1–20.Google Scholar
[4] Chojnacki, W., On group decompositions of bounded cosine sequences. Studia Math. 181 (2007), no. 1, 61–85. http://dx.doi.org/10.4064/sm181-1-5 Google Scholar
[5] Davison, T. M. K., D’Alembert's functional equation on topological groups. Aequationes Math. 76 (2008), no. 1-2, 33–53. http://dx.doi.org/10.1007/s00010-007-2916-4 Google Scholar
[6] Davison, T. M. K., D’Alembert's functional equation on topological monoids. Publ. Math. Debrecen 76 (2009), no. 1-2, 41–66.Google Scholar
[7] Folland, G. B., A Course in Abstract Harmonic Analysis. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.Google Scholar
[8] Stetkær, H., Properties of d’Alembert functions. Aequationes Math. 77 (2009), no. 3, 281–301. http://dx.doi.org/10.1007/s00010-008-2934-x Google Scholar
[9] Yang, D., Factorization of cosine functions on compact connected groups. Math. Z. 254 (2006), no. 4, 655–674. http://dx.doi.org/10.1007/s00209-006-0001-7 Google Scholar
[10] Yang, D., Contributions to the Theory of Functional Equations. Ph.D. Thesis, University of Waterloo, 2006.Google Scholar