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Stability and Linear Independence Associated with Scaling Vectors
1998
SIAM Journal on Mathematical Analysis
In this paper, we discuss stability and linear independence of the integer translates of a scaling vector Φ = (φ 1 , · · · , φ r ) T , which satisfies a matrix refinement equation where (P k ) is a finite matrix sequence. We call P (z) = 1 2 P k z k the symbol of Φ. Stable scaling vectors often serve as generators of multiresolution analyses (MRA) and therefore play an important role in the study of multiwavelets. Most useful MRA generators are also linearly independent. The purpose of this
doi:10.1137/s003614109630330x
fatcat:mbja5vwumrahtku2ni6cchivi4