@article{0ebd0c164f1a48c2b85f6d38709db740,
title = "On the Regularity of Matrix Refinable Functions",
author = "Qingtang Jiang",
note = "It is shown that the transition operator \$\textbackslash{}T\$ associated with the matrix refinement mask \$\textbackslash{}p(\textbackslash{}go )=2\textasciicircum{}\{-d\}\textbackslash{}Sigma\_\{\textbackslash{}alpha \textbackslash{}in [0,N]\textasciicircum{}d\} \textbackslash{}p\_\{\textbackslash{}alpha\}\textbackslash{}hbox\{exp\}(-i\textbackslash{}alpha \textbackslash{}go )\$ is equivalent to the matrix \$(2\textasciicircum{}\{-d\}\textbackslash{}a \_\{2i-j\})\_\{i, j\}\$ with \$\textbackslash{}a \_j=\textbackslash{}Sigma\_\{\textbackslash{}gk \textbackslash{}in [0, N]\textasciicircum{}d\}\textbackslash{}p \_\{\textbackslash{}gk -j\}\textbackslash{}otimes \textbackslash{}p\_\{\textbackslash{}gk\}\$ and \$\textbackslash{}p \_\{\textbackslash{}gk -j\}\textbackslash{}otimes \textbackslash{}p\_\{\textbackslash{}gk\}\$ denoting the Kronecker product of matrices \$\textbackslash{}p \_\{\textbackslash{}gk -j\}\$, \$\textbackslash{}p\_\{\textbackslash{}gk\}\$.",
year = "1998",
month = sep,
language = "American English",
volume = "29",
journal = "SIAM Journal on Mathematical Analysis",
}