Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Decay of Fourier coefficients for Furstenberg measures
HTML articles powered by AMS MathViewer

by Tien-Cuong Dinh, Lucas Kaufmann and Hao Wu
Trans. Amer. Math. Soc. 376 (2023), 6873-6926
DOI: https://doi.org/10.1090/tran/8882
Published electronically: July 20, 2023

Abstract:

Let $\nu$ be the Furstenberg measure associated with a non-elementary probability measure $\mu$ on $SL_2(\mathbb {R})$. We show that, when $\mu$ has a finite second moment, the Fourier coefficients of $\nu$ tend to zero at infinity. In other words, $\nu$ is a Rajchman measure. This improves a recent result of Jialun Li.
References
Similar Articles
Bibliographic Information
  • Tien-Cuong Dinh
  • Affiliation: Department of Mathematics, National University of Singapore - 10, Lower Kent Ridge Road, Singapore 119076, Singapore
  • MR Author ID: 608547
  • Email: matdtc@nus.edu.sg
  • Lucas Kaufmann
  • Affiliation: Center for Complex Geometry, Institute for Basic Science (IBS) - 55, Expo-ro, Yuseong-gu, Daejeon 34126, South Korea; and Institut Denis Poisson, CNRS, Université d’Orléans, Rue de Chartres B.P. 6759, 45067 Orléans Cedex 2, France
  • MR Author ID: 1224314
  • ORCID: 0000-0001-9043-4862
  • Email: lucas.kaufmann@univ-orleans.fr
  • Hao Wu
  • Affiliation: Department of Mathematics, National University of Singapore - 10, Lower Kent Ridge Road, Singapore 119076, Singapore
  • Email: matwu@nus.edu.sg
  • Received by editor(s): March 31, 2022
  • Received by editor(s) in revised form: November 25, 2022
  • Published electronically: July 20, 2023
  • Additional Notes: This work was supported by the NUS and MOE grants AcRF Tier 1 R-146-000-259-114, R-146-000-299-114 and MOE-T2EP20120-0010. The second author was supported by the Institute for Basic Science (IBS-R032-D1)
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 6873-6926
  • MSC (2020): Primary 60B15, 60B20, 60K15; Secondary 42A16, 37C30
  • DOI: https://doi.org/10.1090/tran/8882
  • MathSciNet review: 4636680