258 research outputs found
Some equations relating multiwavelets and multiscaling functions
The local trace function introduced in \cite{Dut} is used to derive equations
that relate multiwavelets and multiscaling functions in the context of a
generalized multiresolution analysis, without appealing to filters. A
construction of normalized tight frame wavelets is given. Particular instances
of the construction include normalized tight frame and orthonormal wavelet
sets
Harmonic Analysis of Signed Ruelle Transfer Operators
Motivated by wavelet analysis, we prove that there is a one-to-one
correspondence between the following data: Solutions to where is a
certain non-positive Ruelle transfer operator; Operators that intertwine a
certain class of representations of the -algebra on two
unitary generators , subject to the relation This
correspondence enables us to give a criterion for the biorthogonality of a pair
of scaling functions and calculate all solutions of the equation in
some concrete cases.Comment: 24 page
Weighted Fourier frames on fractal measures
We generalize an idea of Picioroaga and Weber to construct Paseval frames of
weighted exponential functions for self-affine measures
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