New look at the constructions of multiwavelet frames

Hong Oh Kim; Rae Young Kim; Jae Kun Lim

doi:10.4134/BKMS.2010.47.3.563

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(3): 563-573

Printed May 1, 2010

https://doi.org/10.4134/BKMS.2010.47.3.563

New look at the constructions of multiwavelet frames

Hong Oh Kim, Rae Young Kim, and Jae Kun Lim

Korea Advanced Institute of Science and Technology, Yeungnam University, and Hankyong National University

Abstract

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Abstract

Using the fiberization technique of a shift-invariant space and the matrix characterization of the decomposition of a shift-invariant space of finite length into an orthogonal sum of singly generated shift-invariant spaces, we show that the main result in [13] can be interpreted as a statement about the length of a shift-invariant space, and give a more natural construction of multiwavelet frames from a frame multiresolution analysis of $L^2({\mathbb R}^d)$.

Keywords: wavelet, frame, multiresolution analysis, shift-invariant space

MSC numbers: 42C15, 42C40