|
|||||
 |
|
|
|
|
|
|
|
Fourier decay of
self-similar measures and self-similar sets of uniqueness
Péter P. Varjú and Han Yu |
|
Vol. 15 (2022), No. 3, 843–858
|
Abstract |
|
We investigate the Fourier transform of self-similar measures on . We provide quantitative decay rates of Fourier transform of some self-similar measures. Our method is based on random walks on lattices and Diophantine approximation in number fields. We also completely identify all self-similar sets which are sets of uniqueness. This generalizes a classical result of Salem and Zygmund. |
PDF Access Denied
We have not been able to recognize your IP address
3.149.255.162
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
Rajchman measure, Fourier decay of self-similar measures,
sets of uniqueness, digit changes
|
Mathematical Subject Classification
Primary: 11A63, 28A80, 42A16
|
Milestones
Received: 4 May 2020
Revised: 2 September 2020
Accepted: 27 October 2020
Published: 10 June 2022
|
Authors |
| Péter P. Varjú | |
| Centre for Mathematical
Sciences University of Cambridge Cambridge United Kingdom |
|
| Han Yu | |
| Centre for Mathematical
Sciences University of Cambridge Cambridge United Kingdom |
|
