Title

Iterative Approximations Of Exponential Bases On Fractal Measures

Keywords

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

Abstract

For some fractal measures it is a very difficult problem in general to prove the existence of spectrum (respectively, frame, Riesz and Bessel spectrum). In fact there are examples of extremely sparse sets that are not even Bessel spectra. In this article, we investigate this problem for general fractal measures induced by iterated function systems (IFS). We prove some existence results of spectra associated with Hadamard pairs. We also obtain some characterizations of Bessel spectrum in terms of finite matrices for affine IFS measures, and one sufficient condition of frame spectrum in the case that the affine IFS has no overlap. © 2012 Taylor and Francis Group, LLC.

Publication Date

1-1-2012

Publication Title

Numerical Functional Analysis and Optimization

Volume

33

Issue

7-9

Number of Pages

928-950

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/01630563.2012.682129

Socpus ID

84864685085 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84864685085

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