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The Spectral Radius Formula for Fourier–Stieltjes Algebras

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  22 July 2019

Przemysław Ohrysko  and
Maria Roginskaya
Przemysław Ohrysko
Affiliation:
Chalmers University of Technology and the University of Gothenburg Email: [email protected]@chalmers.se
Maria Roginskaya
Affiliation:
Chalmers University of Technology and the University of Gothenburg Email: [email protected]@chalmers.se
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Abstract

In this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier–Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no non-trivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier–Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.

Keywords

measure algebraFourier–Stieltjes algebra

MSC classification

Primary: 43A10: Measure algebras on groups, semigroups, etc.
Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 269 - 275
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Supported by foundations managed by The Royal Swedish Academy of Sciences.

References

Anoussis, M. and Gatzouras, G., A spectral radius formula for the Fourier transform on compact groups and applications to random walks. Adv. Math. 180(2004), 425–443. https://doi.org/10.1016/j.aim.2003.11.001Google Scholar
Arsac, G., Sur l’espace de Banach engendré par les coefficients d’une représentation unitaire. Publ. Dép. Math. (Lyon) 13(1976), 1–101.Google Scholar
Brown, G. and Moran, W., On orthogonality of Riesz products. Math. Proc. Camb. Phil. Soc. 76(1974), 173–181. https://doi.org/10.1017/s0305004100048830Google Scholar
Eymard, P., L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92(1964), 181–236.Google Scholar
Graham, C. C. and McGehee, O. C., Essays in commutative harmonic analysis. Springer-Verlag, New York, 1979.Google Scholar
Kaniuth, E. and Lau, Anthony T. M., Fourier and Fourier–Stieltjes algebras on locally compact Abelian groups, Mathematical Surveys and Monographs, 231, American Mathematical Society, Providence, RI, 2018.Google Scholar
Ohrysko, P. and Wasilewski, M., Spectral theory of Fourier–Stieltjes algebras. J. Math. Anal. Appl. 473(2019), 174–200. https://doi.org/10.1016/j.jmaa.2018.12.040Google Scholar
Rudin, W., Fourier analysis on groups. John Wiley, New York, 1990. https://doi.org/10.1002/9781118165621Google Scholar
Żelazko, W., Banach algebras. Elsevier, Amsterdam, 1973.Google Scholar