Title

Bessel Sequences Of Exponentials On Fractal Measures

Keywords

Bessel sequence; Beurling dimension; Fractal; Frame; Iterated function system; Riesz basic sequence

Abstract

Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L2(ν). We prove that any fractal measure μ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in L2(μ) such that the frequencies have positive Beurling dimension. © 2011.

Publication Date

11-1-2011

Publication Title

Journal of Functional Analysis

Volume

261

Issue

9

Number of Pages

2529-2539

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2011.06.018

Socpus ID

80052085612 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/80052085612

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