Spectrality of infinite Bernoulli convolutions

DOI10.1016/j.jfa.2015.05.008zbMath1320.28011OpenAlexW261973196MaRDI QIDQ2355448

Hai-Xiong Li, Xing-Gang He, Li-Xiang An

Publication date: 23 July 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2015.05.008

zbMATH Keywords

spectrumspectral measureRamsey theoremself-similarBorel probability measureorthonormal basis of exponential functionsinfinite Bernoulli convolution

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fractals (28A80)

Related Items (37)

Spectral structure of planar self-similar measures with four-element digit set ⋮ Spectrality of infinite convolutions with three-element digit sets ⋮ Spectra of Bernoulli convolutions and random convolutions ⋮ Scaling of spectra of a class of random convolution on \(\mathbb{R}\) ⋮ SPECTRALITY AND NON-SPECTRALITY OF PLANAR SELF-SIMILAR MEASURES WITH FOUR-ELEMENT DIGIT SETS ⋮ Spectral property of certain fractal measures ⋮ Spectral properties of certain Moran measures with consecutive and collinear digit sets ⋮ Weak convergence and spectrality of infinite convolutions ⋮ Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets ⋮ The existence of Fourier basis for some Moran measures ⋮ The cardinality of orthogonal exponentials of planar self-affine measures with two-element digit set ⋮ A characterization on the spectra of self-affine measures ⋮ Tree structure of spectra of spectral self-affine measures ⋮ Spectrality of homogeneous Moran measures on \(\mathbb{R}^n\) ⋮ On the Fourier orthonormal bases of a class of self-similar measures on \(\mathbb{R}^n\) ⋮ Spectrality of Moran-Sierpinski type measures ⋮ On the spectra of a class of self-affine measures on \(\mathbb{R}^2\) ⋮ Spectrality of Moran measures with finite arithmetic digit sets ⋮ Spectrality of Moran-type Bernoulli convolutions ⋮ Spectrality of random convolutions generated by finitely many Hadamard triples ⋮ Spectrality of Moran measures with four-element digit sets ⋮ Unnamed Item ⋮ Uniformity of spectral self-affine measures ⋮ Unnamed Item ⋮ Spectrality of a class of Cantor-Moran measures ⋮ Spectral measures generated by arbitrary and random convolutions ⋮ On the Fourier orthonormal bases of Cantor-Moran measures ⋮ Spectral property of self-affine measures on \(\mathbb{R}^n\) ⋮ Spectral properties of a class of Moran measures ⋮ THE CARDINALITY OF ORTHOGONAL EXPONENTIAL FUNCTIONS ON THE SPATIAL SIERPINSKI GASKET ⋮ Multiple spectra of self-similar measures with three digits on \(\mathbb{R}\) ⋮ Non-spectral problem on infinite Bernoulli convolution ⋮ Spectrality of a class of Moran measures ⋮ Spectral structure and spectral eigenvalue problems of a class of self-similar spectral measures ⋮ Number theoretic related to the scaling spectrum of self-similar measure with three element digit sets ⋮ Spectral property of a class of Moran measures on \(\mathbb{R}\) ⋮ SPECTRAL EIGENVALUE PROBLEMS OF SELF-SIMILAR MEASURES WITH CONSECUTIVE DIGITS

Cites Work

• Unnamed Item
• A problem on completeness of exponentials
• Spectral property of Cantor measures with consecutive digits
• When does a Bernoulli convolution admit a spectrum?
• A class of spectral Moran measures
• On the Beurling dimension of exponential frames
• Spectra of a class of self-affine measures
• On Fourier frame of absolutely continuous measures
• \(\mu _{m,d}\)-orthogonality and compatible pair
• Fourier frequencies in affine iterated function systems
• Spectral property of the Bernoulli convolutions
• On the spectra of a Cantor measure
• Dense analytic subspaces in fractal \(L^2\)-spaces
• Remarks on ``Dense analytic subspaces in fractal \(L^2\)-spaces by P. E. T. Jorgensen and S. Pedersen
• Spectral sets and factorizations of finite abelian groups
• Commuting self-adjoint partial differential operators and a group theoretic problem
• On spectral Cantor measures
• Fourier frames
• Fuglede's conjecture is false in 5 and higher dimensions
• Exponential spectra in \(L^2(\mu)\)
• Multi-tiling and Riesz bases
• Uniformity of measures with Fourier frames
• On spectral \({N}\)-Bernoulli measures
• Convergence of mock Fourier series
• Necessary density conditions for sampling an interpolation of certain entire functions
• Fuglede’s conjecture for a union of two intervals
• Tiles with no spectra
• The Factorisation of the rectangular distribution

This page was built for publication: Spectrality of infinite Bernoulli convolutions