On iterates of convolutions

Foguel, Shaul R.

doi:10.1090/S0002-9939-1975-0374816-X

On iterates of convolutions
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by Shaul R. Foguel PDF

Proc. Amer. Math. Soc. 47 (1975), 368-370 Request permission

Abstract:

Let $\mu$ be a signed measure, of total variation one, on a locally compact Abelian group. We study in this note the ideal $I = \{ \tau :\tau \ll m\;and\; ||{\mu ^n} \ast \tau || \to 0\}$ where $m$ is the Haar measure.

References

Antoine Brunel, Pierre Crépel, Yves Guivarc’h, and Michael Keane, Marches aléatoires récurrentes sur les groupes localement compacts, C. R. Acad. Sci. Paris Sér. A-B 275 (1972), A1359–A1361 (French). MR 317415
William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
S. R. Foguel and B. Weiss, On convex power series of a conservative Markov operator, Proc. Amer. Math. Soc. 38 (1973), 325–330. MR 313476, DOI 10.1090/S0002-9939-1973-0313476-9
Donald S. Ornstein, Random walks. I, II, Trans. Amer. Math. Soc. 138 (1969), 1-43; ibid. 138 (1969), 45–60. MR 0238399, DOI 10.1090/S0002-9947-1969-0238399-9
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834