Bessel sequences of exponentials on fractal measures

    Authors

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

    Comments

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    Abbreviated Journal Title

    J. Funct. Anal.

    Keywords

    Fractal; Iterated function system; Frame; Bessel sequence; Riesz basic; sequence; Beurling dimension; ITERATED FUNCTION SYSTEMS; MOCK FOURIER-SERIES; BEURLING DIMENSION; FRAMES; SUBSPACES; Mathematics

    Abstract

    Jorgensen and Pedersen have proven that a certain fractal measure v has no infinite set of complex exponentials which form an orthonormal set in L(2)(nu). We prove that any fractal measure mu 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 L(2)(mu) such that the frequencies have positive Beurling dimension. Published by Elsevier Inc.

    Journal Title

    Journal of Functional Analysis

    Volume

    261

    Issue/Number

    9

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    2529

    Last Page

    2539

    WOS Identifier

    WOS:000294703500007

    ISSN

    0022-1236

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