Related papers: Perturbation of frames in Banach spaces
In this paper we establish inhomogeneous coorbit spaces related to the continuous shearlet transform and the weighted Lebesgue spaces $L_{p,v}, p\geq 1,$ for certain weights $v$. We present an inhomogeneous shearlet frame for…
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system.…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach…
This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is…
G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…
A family of the Block Matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patch-wise image modeling [1], [2]. In this paper we construct analysis and synthesis frames,…
We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding different notions of bases in Banach spaces and lattices. For the…
This note has two objectives. The first objective is show that, even if a separable Banach space does not have a Schauder basis (S-basis), there always exists Hilbert spaces $\mcH_1$ and $\mcH_2$, such that $\mcH_1$ is a continuous dense…
The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The…
We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of…
We develop deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors, in a spirit similar to classical results for matrices such as those due to Weyl, Davis, Kahan and Wedin. Our bounds…
A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur.…
We analyze the final state sensitivity of nonlocal networks with respect to initial conditions of their units. By changing the initial conditions of a single network unit, we perturb an initially synchronized state. Depending on the…
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…
When the vacuum Einstein equations are formulated in terms of a frame, rather than a metric, can one perturb solutions with a degenerate frame into ones with a nondegenerate frame? In examples we point out that one can encounter issues…
We study atomic decompositions in Fr\'echet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete atomic decompositions on a locally convex space, study the duality of these two concepts and…
Rough surface scattering problems are always very challenging both theoretically and numerically. In this paper, we adopt the Bloch transform and the perturbation theory to investigate a special case, i.e., when the rough surface is a…