Fourier decay for self-similar measures

Boris Solomyak

doi:10.1090/proc/15515

Fourier decay for self-similar measures

Boris Solomyak

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have a power decay of the Fourier transform at infinity. In the homogeneous case, when all contraction ratios are equal, this is essentially due to Erdos and Kahane. In the non-homogeneous case the difficulty we have to overcome is the apparent lack of convolution structure.

Original language	English
Pages (from-to)	3277-3291
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	8
DOIs	https://doi.org/10.1090/proc/15515
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 American Mathematical Society

Funding

Received by the editors July 30, 2019, and, in revised form, September 22, 2020. 2020 Mathematics Subject Classification. Primary 28A80, 42A16, 60G18. This research was supported by the Israel Science Foundation Grant 396/15.

Funders	Funder number
Israel Science Foundation	396/15

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10.1090/proc/15515

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Fourier decay for self-similar measures

Abstract

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