The Spectral Radius Formula for Fourier–Stieltjes Algebras
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 269-275

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/S0008439519000213
Mots-clés : measure algebra, Fourier–Stieltjes algebra
Ohrysko, Przemysław; Roginskaya, Maria. The Spectral Radius Formula for Fourier–Stieltjes Algebras. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 269-275. doi: 10.4153/S0008439519000213
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[AG] 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.2003.11.001 Google Scholar

[A] 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

[BM1] Brown, G. and Moran, W., On orthogonality of Riesz products. Math. Proc. Camb. Phil. Soc. 76(1974), 173–181. https://doi.org/10.1017/s0305004100048830 Google Scholar

[Ey] Eymard, P., L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92(1964), 181–236. Google Scholar

[GM] Graham, C. C. and Mcgehee, O. C., Essays in commutative harmonic analysis. Springer-Verlag, New York, 1979. Google Scholar

[KL] 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

[OW] 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.2018.12.040 Google Scholar

[R] Rudin, W., Fourier analysis on groups. John Wiley, New York, 1990. https://doi.org/10.1002/9781118165621 Google Scholar

[Ż] Żelazko, W., Banach algebras. Elsevier, Amsterdam, 1973. Google Scholar

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