ITERATIVE APPROXIMATIONS OF EXPONENTIAL BASES ON FRACTAL MEASURES

    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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