Fourier decay for homogeneous self-affine measures

Boris Solomyak

doi:10.4171/JFG/119

Fourier decay for homogeneous self-affine measures

Boris Solomyak

Department of Mathematics

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

6 Scopus citations

Abstract

We show that for Lebesgue almost all d-tuples (θ₁;...; θ_d), with |θ_j| > 1, any self-affine measure for a homogeneous non-degenerate iterated function system {Ax + a_j}^m_j=1 in R^d, where A^-1 is a diagonal matrix with the entries (θ₁;...; θ_d), has power Fourier decay at infinity.

Original language	English
Pages (from-to)	193-206
Number of pages	14
Journal	Journal of Fractal Geometry
Volume	9
Issue number	1-2
DOIs	https://doi.org/10.4171/JFG/119
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 European Mathematical Society.

Funding

Supported in part by the Israel Science Foundation grant 911/19.

Funders	Funder number
Israel Science Foundation	911/19

Keywords

Erdos–Kahane ̋ method
Fourier decay
Self-affine measure

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10.4171/JFG/119

Cite this

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title = "Fourier decay for homogeneous self-affine measures",

abstract = "We show that for Lebesgue almost all d-tuples (θ1;...; θd), with |θj| > 1, any self-affine measure for a homogeneous non-degenerate iterated function system \{Ax + aj\}mj=1 in Rd, where A-1 is a diagonal matrix with the entries (θ1;...; θd), has power Fourier decay at infinity.",

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N2 - We show that for Lebesgue almost all d-tuples (θ1;...; θd), with |θj| > 1, any self-affine measure for a homogeneous non-degenerate iterated function system {Ax + aj}mj=1 in Rd, where A-1 is a diagonal matrix with the entries (θ1;...; θd), has power Fourier decay at infinity.

AB - We show that for Lebesgue almost all d-tuples (θ1;...; θd), with |θj| > 1, any self-affine measure for a homogeneous non-degenerate iterated function system {Ax + aj}mj=1 in Rd, where A-1 is a diagonal matrix with the entries (θ1;...; θd), has power Fourier decay at infinity.

KW - Erdos–Kahane ̋ method

KW - Fourier decay

KW - Self-affine measure

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ER -

Fourier decay for homogeneous self-affine measures

Abstract

Bibliographical note

Funding

Keywords

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