On Stable Refinable Function Vectors with Arbitrary Support
given at strobl07 (17.06.07)
Refinable function vectors with arbitrary support are considered.
In particular necessary conditions for stability are given and a characterization
of the symbol associated with a stable refinable function vector
in terms of the transfer operator is provided:
this is a generalization of Gundy's theorem to the vector case.
The proof adapts the tools provided in Saliani,
On stability and orthogonality of refinable functions,
Appl. Comp. Harm. Anal., 21, (2006), 254-261.
Though complications arise from noncommuting
matrix products, the fundamental ideas are the same.