Related papers: Parseval frames for ICC groups
A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…
This article explores the problem of modifying the subspaces of a fusion frame in order to construct a Parseval fusion frame. In this respect, the notion of scalability is extended to the fusion frame setting. Then, scalable fusion Riesz…
In this note, we prove some results related to small perturbations of a frame for a Hilbert space $\mathcal{H}$ in order to have a woven pair for $\mathcal{H}$. Our results complete those known in the literature. In addition we study a…
We give an equivariant version of Packer and Rieffel's theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analyses. The scaling functions that generate a projective multiresolution…
Controlled frames have been recently introduced in Hilbert spaces to improve the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper, unlike the cross-Gram matrix of two different sequences which…
A semigroup generated by two dimensional $C^{1+\alpha}$ contracting maps is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives of…
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to…
Given an orthonormal basis $ {\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors $ {\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets $ {\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\,…
We explore transversals of finite index subgroups of finitely generated groups. We show that when $H$ is a subgroup of a rank $n$ group $G$ and $H$ has index at least $n$ in $G$ then we can construct a left transversal for $H$ which…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case…
We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…
Let $N$ be a step two connected and simply connected non commutative nilpotent Lie group which is square-integrable modulo the center. Let $Z$ be the center of $N$. Assume that $N=P\rtimes M$ such that $P$, and $M$ are simply connected,…
We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
We study singly-generated wavelet systems on $\Bbb R^2$ that are naturally associated with rank-one wavelet systems on the Heisenberg group $N$. We prove a necessary condition on the generator in order that any such system be a Parseval…
While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…
We introduce the term "protonormal" to refer to a subgroup H of a group G such that for every x in G the subgroups x^{-1}Hx and H commute as sets. If moreover (G,H) is a Hecke pair we show that the Hecke algebra H(G,H) is generated by the…
In this paper, we view matrix frames as representations of quivers and study them within the general framework of quiver invariant theory. We are thus led to consider the large class of semi-stable matrix frames. Within this class, we are…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…