Families of spectral sets for Bernoulli convolutions
Palle Jorgensen (University of Iowa), Keri Kornelson (University of, Oklahoma), Karen Shuman (Grinnell College)
TL;DR
This paper explores the harmonic analysis of Bernoulli measures, identifying orthonormal Fourier bases and maximal Fourier families, advancing understanding of their spectral properties.
Contribution
It introduces new orthonormal Fourier bases and maximal Fourier families for Bernoulli measures using contractive transfer operators.
Findings
Identified orthonormal Fourier bases for specific Bernoulli measures
Constructed maximal Fourier families not forming bases
Enhanced understanding of spectral structures of Bernoulli convolutions
Abstract
In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Advanced Harmonic Analysis Research