LAUSR

A Characterization on the Spectra of Self-Affine Measures

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1 Published in 2019 at "Journal of Fourier Analysis and Applications"

DOI: 10.1007/s00041-018-9621-7

Abstract: A discrete set $$\Lambda \subseteq {\mathbb {R}}^d$$Λ⊆Rd is called a spectrum for the probability measure $$\mu $$μ if the family of functions $$\{e^{2 \pi i \langle \lambda ,\, x\rangle }: \lambda \in \Lambda \}$${e2πi⟨λ,x⟩:λ∈Λ} forms… read more here.

Keywords: lambda; characterization spectra; spectra self; affine measures ... See more keywords

Non-spectrality of self-affine measures

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0 Published in 2019 at "Journal of Functional Analysis"

DOI: 10.1016/j.jfa.2019.05.015

Abstract: Abstract Under some supportive evidences of known results about non-spectral self-affine measures, Li proposed a conjecture in [18] (J. Funct. Anal. 255, 2008), which is so-called “non-spectral conjecture”. In this paper, we prove that Li's… read more here.

Keywords: self affine; non spectrality; affine measures; non spectral ... See more keywords

Spectrality of a class of self-affine measures on R2

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1 Published in 2021 at "Nonlinearity"

DOI: 10.1088/1361-6544/ac2493

Abstract: In this work, we study the spectral property of a class of self-affine measures μ M,D on R2 generated by an expanding real matrix M=diagρ1−1,ρ2−1 and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with αi−2βi∉3Z ,… read more here.

Keywords: affine measures; class self; self affine;

DOUBLING PROPERTIES OF SELF-AFFINE MEASURES SUPPORTED ON GATZOURAS–LALLEY FRACTALS

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0 Published in 2019 at "Fractals"

DOI: 10.1142/s0218348x19501275

Abstract: In this paper, we study the doubling properties of self-affine measures supported on a class of self-affine sets named Gatzouras–Lalley sets. First, we show that every self-affine measure is doubli... read more here.

Keywords: properties self; measures supported; affine measures; doubling properties ... See more keywords