Related papers: Optimal Dynamical Frames
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
We answer a number of open problems in frame theory concerning the decomposition of frames into linearly independent and/or spanning sets. We prove that in finite dimensional Hilbert spaces, Parseval frames with norms bounded away from 1…
Let $\hil$ be a finite dimensional (real or complex) Hilbert space and let $\{a_i\}_{i=1}^\infty$ be a non-increasing sequence of positive numbers. Given a finite sequence of vectors $\f$ in $\hil$ we find necessary and sufficient…
Dynamical Sampling of frames and tensor products are important topics in harmonic analysis. This paper combines the concepts of dynamical sampling of frames and the Carleson condition in the tensor product of Hardy spaces. Initially we…
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this…
We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant…
We consider sequences in a Hilbert space $\mathcal H$ of the form $(T^nf_0)_{n\in I},$ with a linear operator $T$, the index set being either $I = \mathbb N$ or $I = \mathbb Z$, a vector $f_0\in \mathcal H$, and answer the following two…
This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining…
Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame in…
Dynamic patterns are characterized by complex spatial and motion patterns. Understanding dynamic patterns requires a disentangled representational model that separates the factorial components. A commonly used model for dynamic patterns is…
Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…
Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…
$E$-frames are a new generalization for the concept of frames for $\mathcal{H}$, where $E$ is an infinite invertible complex matrix mapping on $\bigoplus_{n=1}^{\infty}\mathcal{H}$. This article is dedicated to investigating some notions…
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…
We propose Framer for interactive frame interpolation, which targets producing smoothly transitioning frames between two images as per user creativity. Concretely, besides taking the start and end frames as inputs, our approach supports…
A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose integer translates…
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…
Let Y={f(i), Af(i),..., A^{li} f(i): i in Omega}, where A is a bounded operator on l^2(I). The problem under consideration is to find necessary and sufficient conditions on A, Omega, {l_i:i in Omega} in order to recover any f \in l^2(I)…