Bessel sequences of exponentials on fractal measures

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.