Dimension functions, scaling sequences, and wavelet sets

• Autorzy: Arambašić Ljiljana , Damir Bakić , Rajna Rajić
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 42C15: General harmonic expansions, frames

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 1
• Strony: 1-32

Daty

wydano

2010

Twórcy

autor

Arambašić Ljiljana

• Department of Mathematics, University of Zagreb, Bijenička c. 30, 10000 Zagreb, Croatia

autor

Damir Bakić

• Department of Mathematics, University of Zagreb, Bijenička c. 30, 10000 Zagreb, Croatia

autor

Rajna Rajić

• Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia

Identyfikatory

DOI

10.4064/sm198-1-1