Isomorphism in Wavelets

Xingde Dai; Wei Huang

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arXiv · 1904.07139

Isomorphism in Wavelets

Xingde Dai·Wei Huang

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Abstract

Two scaling functions $φ_A$ and $φ_B$ for Parseval frame wavelets are algebraically isomorphic, $φ_A \simeq φ_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be $d\times d$ and $s\times s$ \thematrix matrices with $d, s\geq 1$ respectively and let $φ_A$ be a scaling function associated with matrix $A$ and generated by a finite solution. There always exists a scaling function $φ_B$ associated with matrix $B$ such that \begin{equation*} φ_B \simeq φ_A. \end{equation*} An example shows that the assumption on the finiteness of the solutions can not be removed.

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BibTeX RIS

Xingde Dai, Wei Huang. 2019-04-15. Isomorphism in Wavelets. https://arxiv.org/abs/1904.07139

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