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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