Expand all Collapse all | Results 1 - 7 of 7 |
1. CMB 2013 (vol 57 pp. 463)
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 Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 |
2. CMB 2013 (vol 57 pp. 254)
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 UEP-type wavelet systems that
can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet
system. We derive a condition that is necessary for the extension of a UEP-type
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 |
3. CMB 2013 (vol 56 pp. 729)
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
pseudo-lattice $\Gamma$. 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 super-representation 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, Baumslag-Solitar group, shearlet Categories:43A65, 42C40, 42C15 |
4. CMB 2008 (vol 51 pp. 348)
The Reconstruction Property in Banach Spaces and a Perturbation Theorem Perturbation theory is a fundamental tool in Banach space theory.
However, the applications of the classical results
are limited by the fact that they force the
perturbed sequence to be equivalent to the given sequence.
We will develop
a more general perturbation theory that does not force equivalence of the
sequences.
Category:42C15 |
5. CMB 2007 (vol 50 pp. 85)
Classification of Finite Group-Frames and Super-Frames 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, group-frames, frame representations, disjoint frames Categories:42C15, 46C05, 47B10 |
6. CMB 1999 (vol 42 pp. 37)
Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace Recent work of Ding and Huang shows that if we perturb a bounded
operator (between Hilbert spaces) which has closed range, then the
perturbed operator again has closed range. We extend this result by
introducing a weaker perturbation condition, and our result is then
used to prove a theorem about the stability of frames for a subspace.
Category:42C15 |
7. CMB 1998 (vol 41 pp. 398)
Band-limited 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
band-limited. We do this by showing that we can adapt the
construction of the Lemari\'e-Meyer wavelets \cite{LM} that
is found in \cite{BSW} so that we obtain band-limited,
$C^\infty$-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 |