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> Volume 5, Issue 1
Preprints: Two papres on multiwavelets from Strela

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Vasily Strela (strela@math.mit.edu) Guest

Posted: Tue Dec 03, 2002 4:15 pm Subject: Preprints: Two papres on multiwavelets from Strela




Preprints: Two papres on multiwavelets from Strela
Title : Multiwavelets: Regularity, Orthogonality and Symmetry via
Twoscale Similarity Transform
Author : Vasily Strela, strela@math.mit.edu
Abstract: An important object in wavelet theory is the scaling
function $phi(t)$, satisfying a dilation equation $phi(t)=sum C_k
phi(2tk)$. Properties of a scaling function are closely related to
the properties of the symbol or mask $P(omega)=sum C_k e^{iomega
k}$. The approximation order provided by $phi(t)$ is the number of
zeros of $P(omega)$ at $omega = pi$, or in other words the number
of factors $(1+e^{iomega})$ in $P(omega)$. In the case of
multiwavelets $P(omega)$ becomes a matrix trigonometric
polynomial. The factors $(1+e^{iomega})$ are replaced by a matrix
factorization of nn $P(omega)$, which defines the approximation order
of the multiscaling function. This matrix factorization is based on
the twoscale similarity transform (TST). In this paper we study
properties of the TST and show how it is connected with the theory of
multiwavelets. This approach leads us to new results on regularity,
symmetry and orthogonality of multiscaling functions and opens an
easy way to their construction.
Title : Construction of MultiScaling Functions with
Approximation and Symmetry
Authors : Gerlind Plonka, gerlind.plonka@mathematik.unirostock.d400.de
Vasily Strela, strela@math.mit.edu
Abstract: This paper presents a new and efficient way to create
multiscaling functions with given approximation order, regularity,
symmetry and short support. Previous techniques were operating in the
time domain and required the solution of large systems of nonlinear
equations. By switching to the frequency domain and employing the
latest results of the multiwavelet theory we were able to elaborate a
simple and efficient method of construction of multiscaling
functions. Our algorithm is based on a recently found factorization
of the refinement mask through the twoscale similarity transform
(TST). Theoretical results and new examples
Preprints can be obtained by writing to strela@math.mit.edu 





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