1. CMB 2016 (vol 59 pp. 528)
 Jahan, Qaiser

Characterization of Lowpass Filters on Local Fields of Positive Characteristic
In this article, we give necessary and sufficient conditions
on a function to be a lowpass filter on a local field $K$ of
positive characteristic associated to the scaling function for
multiresolution analysis of $L^2(K)$. We use probability and
martingale methods to provide such a characterization.
Keywords:multiresolution analysis, local field, lowpass filter, scaling function, probability, conditional probability and martingales Categories:42C40, 42C15, 43A70, 11S85 

2. CMB 2013 (vol 57 pp. 463)
 Bownik, Marcin; Jasper, John

Constructive Proof of Carpenter's Theorem
We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
Keywords:diagonals of projections, the SchurHorn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 

3. 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 

4. 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 

5. CMB 2008 (vol 51 pp. 348)
6. CMB 2007 (vol 50 pp. 85)
 Han, Deguang

Classification of Finite GroupFrames and SuperFrames
Given a finite group $G$, we examine the classification of all
frame representations of $G$ and the classification of all
$G$frames, \emph{i.e.,} frames induced by group representations of $G$.
We show that the exact number of equivalence classes of $G$frames
and the exact number of frame representations can be explicitly
calculated. We also discuss how to calculate the largest number
$L$ such that there exists an $L$tuple of strongly disjoint
$G$frames.
Keywords:frames, groupframes, frame representations, disjoint frames Categories:42C15, 46C05, 47B10 

7. CMB 1999 (vol 42 pp. 37)
8. 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 
