Title

ITERATIVE APPROXIMATIONS OF EXPONENTIAL BASES ON FRACTAL MEASURES

Authors

Authors

D. E. Dutkay; D. G. Han;E. Weber

Comments

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Abbreviated Journal Title

Numer. Funct. Anal. Optim.

Keywords

Bessel sequence; Beurling dimension; Fractal; Frame; Iterated function; system; Riesz basic sequence; FUNCTION SYSTEMS; FRAMES; Mathematics, Applied

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.

Journal Title

Numerical Functional Analysis and Optimization

Volume

33

Issue/Number

7-9

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

928

Last Page

950

WOS Identifier

WOS:000307080400010

ISSN

0163-0563

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