A+ CATEGORY SCIENTIFIC UNIT

Dimension functions, scaling sequences, and wavelet sets

Volume 198 / 2010

Arambašić Ljiljana, Damir Bakić, Rajna Rajić Studia Mathematica 198 (2010), 1-32 MSC: 42C15, 42C40. DOI: 10.4064/sm198-1-1

Abstract

The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function $D$ there exists an MSF wavelet whose dimension function coincides with $D$. Our method provides a completely new explicit construction of an admissible generalized multiresolution analysis (and, a posteriori, of a wavelet) from an arbitrary dimension function. Several examples are included.

Authors

  • Arambašić LjiljanaDepartment of Mathematics
    University of Zagreb
    Bijenička c. 30
    10000 Zagreb, Croatia
    e-mail
  • Damir BakićDepartment of Mathematics
    University of Zagreb
    Bijenička c. 30
    10000 Zagreb, Croatia
    e-mail
  • Rajna RajićFaculty of Mining, Geology
    and Petroleum Engineering
    University of Zagreb
    Pierottijeva 6
    10000 Zagreb, Croatia
    e-mail

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