JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Dimension functions, scaling sequences, and wavelet sets

### Tom 198 / 2010

Studia Mathematica 198 (2010), 1-32 MSC: 42C15, 42C40. DOI: 10.4064/sm198-1-1

#### Streszczenie

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.

#### Autorzy

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

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek