Opuscula Math. 32, no. 1 (2012), 21-29
http://dx.doi.org/10.7494/OpMath.2012.32.1.21

Opuscula Mathematica

# Compactly supported multi-wavelets

Wojciech Banaś

Abstract. In this paper we show some construction of compactly supported multi-wavelets in $$L^2(\mathbb{R}^d)$$, $$d \geq 2$$ which is based on the one-dimensional case, when $$d=1$$. We also demonstrate that some methods, which are useful in the construction of wavelets with a compact support at $$d=1$$, can be adapted to higher-dimensional cases if $$A \in M_{d \times d}(\mathbb{Z})$$ is an expansive matrix of a special form.

Keywords: compactly supported multi-wavelet, compactly supported scaling function, multiresolution analysis, expansive matrix.

Mathematics Subject Classification: 42C40.

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• Wojciech Banaś
• Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Krakow, Poland
• Revised: 2011-03-17.
• Accepted: 2011-05-06.