Non-spectral problem on infinite Bernoulli convolution
type: Item
instance of: scholarly article
title: Non-spectral problem on infinite Bernoulli convolution
zbMATH Open document ID: 1499.28014
author: Yanyan Li
published in: Analysis Mathematica
publication date: 2021-08-03T00:00:00Z
review text: The article is devoted to the convolution of measures on \([0, \infty)\) with support in a countable set. Particularly, the infinite Bernoulli convolution \(\mu_{\rho, \{ 0, d_k \}} \) is considered as a family of Dirac measures. For them orthogonal sets and maximal orthogonal sets are studied. They correspond to orthonormal families (or maximal orthonormal families) in \(L^2(\mu_{\rho, \{ 0, d_k \}}, \mathbb{R})\). Conditions on \(\rho \) are found for which such sets exist. Examples are provided.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 7377549
zbMATH Keywords: infinite Bernoulli convolution
zbMATH Keywords: spectral measure
zbMATH Keywords: orthogonal exponential functions
zbMATH Keywords: Fourier transform
reviewed by: Sergey V. Ludkovsky
MaRDI profile type: Publication
full work available at URL: s10476-021-0069-7
OpenAlex ID: W3123207774
cites work: Spectrality of infinite Bernoulli convolutions
cites work: On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem
cites work: An introduction to frames and Riesz bases
cites work: Spectral property of Cantor measures with consecutive digits
cites work: On spectral \({N}\)-Bernoulli measures
cites work: Spectrality of one dimensional self-similar measures with consecutive digits
cites work: Bessel sequences of exponentials on fractal measures
cites work: Hadamard triples generate self-affine spectral measures
cites work: Analysis of orthogonality and of orbits in affine iterated function systems
cites work: Spectral property of the Bernoulli convolutions
cites work: Dense analytic subspaces in fractal \(L^2\)-spaces
cites work: On spectral Cantor measures
cites work: Non-spectral fractal measures with Fourier frames
cites work: Spectra of a class of self-affine measures
cites work: Non-spectrality of self-affine measures on the spatial Sierpinski gasket
cites work: Non-spectral problem for the planar self-affine measures
cites work: Non-spectral Problem for Some Self-similar Measures
cites work: THE CARDINALITY OF ORTHOGONAL EXPONENTIAL FUNCTIONS ON THE SPATIAL SIERPINSKI GASKET
DOI: 10.1007/S10476-021-0069-7
description: scientific article; zbMATH DE number 7377549