Opuscula Math. 32, no. 1 (2012), 21-29

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
  • Received: 2010-05-06.
  • Revised: 2011-03-17.
  • Accepted: 2011-05-06.
Opuscula Mathematica - cover

Cite this article as:
Wojciech Banaś, Compactly supported multi-wavelets, Opuscula Math. 32, no. 1 (2012), 21-29, http://dx.doi.org/10.7494/OpMath.2012.32.1.21

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