Dimension functions, scaling sequences, and wavelet sets

Arambašić Ljiljana, Damir Bakić, and Rajna Rajić. "Dimension functions, scaling sequences, and wavelet sets." Studia Mathematica 198.1 (2010): 1-32. <http://eudml.org/doc/286116>.

@article{ArambašićLjiljana2010,
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.},
author = {Arambašić Ljiljana, Damir Bakić, Rajna Rajić},
journal = {Studia Mathematica},
keywords = {dimension function; wavelet},
language = {eng},
number = {1},
pages = {1-32},
title = {Dimension functions, scaling sequences, and wavelet sets},
url = {http://eudml.org/doc/286116},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Arambašić Ljiljana
AU - Damir Bakić
AU - Rajna Rajić
TI - Dimension functions, scaling sequences, and wavelet sets
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 1
SP - 1
EP - 32
AB - 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.
LA - eng
KW - dimension function; wavelet
UR - http://eudml.org/doc/286116
ER -