1. CMB 2013 (vol 57 pp. 254)
 Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle
The unitary extension principle (UEP) by Ron and Shen yields a
sufficient condition for the construction of Parseval wavelet frames with
multiple generators. In this paper we characterize the UEPtype wavelet systems that
can be extended to a Parseval wavelet frame by adding just one UEPtype wavelet
system. We derive a condition that is necessary for the extension of a UEPtype
wavelet system to any Parseval wavelet frame with any number of generators, and
prove that this condition is also sufficient to ensure that an extension
with just two generators is possible.
Keywords:Bessel sequences, frames, extension of wavelet Bessel system to tight frame, wavelet systems, unitary extension principle Categories:42C15, 42C40 

2. CMB 2013 (vol 56 pp. 729)
 Currey, B.; Mayeli, A.

The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames
In this work we introduce a class of discrete groups containing
subgroups of abstract translations and dilations, respectively. A
variety of wavelet systems can appear as $\pi(\Gamma)\psi$, where $\pi$ is
a unitary representation of a wavelet group and $\Gamma$ is the abstract
pseudolattice $\Gamma$. We prove a condition in order that a Parseval
frame $\pi(\Gamma)\psi$ can be dilated to an orthonormal basis of the
form $\tau(\Gamma)\Psi$ where $\tau$ is a superrepresentation of
$\pi$. For a subclass of groups that includes the case where the
translation subgroup is Heisenberg, we show that this condition
always holds, and we cite familiar examples as applications.
Keywords:frame, dilation, wavelet, BaumslagSolitar group, shearlet Categories:43A65, 42C40, 42C15 

3. CMB 2013 (vol 56 pp. 745)
 Fu, Xiaoye; Gabardo, JeanPierre

Dimension Functions of SelfAffine Scaling Sets
In this paper, the dimension function of a selfaffine generalized scaling set associated with an $n\times n$ integral expansive dilation $A$ is studied. More specifically, we consider the dimension function of an $A$dilation generalized scaling set $K$ assuming that $K$ is a selfaffine tile satisfying $BK = (K+d_1) \cup (K+d_2)$, where $B=A^t$, $A$ is an $n\times n$ integral expansive matrix with $\lvert \det A\rvert=2$, and $d_1,d_2\in\mathbb{R}^n$. We show that the dimension function of $K$ must be constant if either $n=1$ or $2$ or one of the digits is $0$, and that it is bounded by $2\lvert K\rvert$ for any $n$.
Keywords:scaling set, selfaffine tile, orthonormal multiwavelet, dimension function Category:42C40 

4. CMB 2009 (vol 53 pp. 133)
5. CMB 2004 (vol 47 pp. 389)
6. CMB 1998 (vol 41 pp. 398)
 Dziubański, Jacek; Hernández, Eugenio

Bandlimited wavelets with subexponential decay
It is well known that the compactly supported wavelets cannot belong to
the class $C^\infty({\bf R})\cap L^2({\bf R})$. This is also true for
wavelets with exponential decay. We show that one can construct
wavelets in the class $C^\infty({\bf R})\cap L^2({\bf R})$ that are
``almost'' of exponential decay and, moreover, they are
bandlimited. We do this by showing that we can adapt the
construction of the Lemari\'eMeyer wavelets \cite{LM} that
is found in \cite{BSW} so that we obtain bandlimited,
$C^\infty$wavelets on $\bf R$ that have subexponential decay,
that is, for every $0<\varepsilon<1$, there exits $C_\varepsilon>0$
such that $\psi(x)\leq C_\varepsilon e^{x^{1\varepsilon}}$,
$x\in\bf R$. Moreover, all of its derivatives have also
subexponential decay. The proof is constructive and uses the
Gevrey classes of functions.
Keywords:Wavelet, Gevrey classes, subexponential decay Category:42C15 
