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Frame Wavelets with Compact Supports for L2(Rn)

Research paper by De Yun Yang, Xing Wei Zhou, Zhu Zhi Yuan

Indexed on: 12 Dec '06Published on: 12 Dec '06Published in: Acta Mathematica Sinica, English Series



Abstract

The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For a given n × n real expansive matrix A, the frame-sets with respect to A are a family of sets in Rn. Based on the frame-sets, a class of high-dimensional frame wavelets with analytic forms are constructed, which can be non-bandlimited, or even compactly supported. As an application, the construction is illustrated by several examples, in which some new frame wavelets with compact supports are constructed. Moreover, since the main result of this paper is about general dilation matrices, in the examples we present a family of frame wavelets associated with some non-integer dilation matrices that is meaningful in computational geometry.